[77] **viXra:1809.0550 [pdf]**
*submitted on 2018-09-27 11:59:53*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

The CC conjecture as defined by Lin Fan Mao is not tautologous and hence refuted.

**Category:** General Mathematics

[76] **viXra:1809.0513 [pdf]**
*submitted on 2018-09-24 07:56:20*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

In this note we give some fractals and formulas for Pi: pi=3.1415926535...

**Category:** General Mathematics

[75] **viXra:1809.0511 [pdf]**
*submitted on 2018-09-24 07:59:39*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

Some remarks on a trigonometric integral.

**Category:** General Mathematics

[74] **viXra:1809.0474 [pdf]**
*submitted on 2018-09-22 09:08:19*

**Authors:** Colin James III

**Comments:** Pages.

In bivalent mathematical logic, the unfalsifiable conjecture is not contradictory, and hence tautologous to be a theorem. The theorem by definition is not contradictory, tautologous, and hence unfalsifiable. There is no distinction between the states of unfalsifiable or confirmable as opposed to falsifiable or refutable.

**Category:** General Mathematics

[73] **viXra:1809.0454 [pdf]**
*submitted on 2018-09-20 11:33:44*

**Authors:** Craig Alan Feinstein

**Comments:** Progress in Physics, 2018 (vol. 14), issue 4, pages 213-214

It is generally accepted among scientists that an unfalsifiable theory, a theory which can never conceivably be proven false, can never have any use in science. In this paper, we shall address the question, “Can an unfalsifiable conjecture ever have any use in mathematics?”

**Category:** General Mathematics

[72] **viXra:1809.0452 [pdf]**
*replaced on 2018-09-21 08:28:21*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

The Smarandache multi-space theory (SMT) as based on a Latin square is a vector space (probabilistic) and not bivalent (exact). Therefore SMT is refuted in classical logic.

**Category:** General Mathematics

[71] **viXra:1809.0429 [pdf]**
*submitted on 2018-09-20 00:14:36*

**Authors:** V. Ramachandran

**Comments:** 8 Pages.

V.Ramachandran and C. Sekar introduced one modulo N graceful where N is any positive integer. In the case N = 2, the labelling is odd graceful and in the case N = 1 the labelling is graceful.

**Category:** General Mathematics

[70] **viXra:1809.0428 [pdf]**
*submitted on 2018-09-20 00:16:30*

**Authors:** R.Ponraj, M.Maria Adaickalam

**Comments:** 7 Pages.

A graph with a k-difference cordial labeling is
called a k-difference cordial graph.

**Category:** General Mathematics

[69] **viXra:1809.0427 [pdf]**
*submitted on 2018-09-20 00:17:43*

**Authors:** R.Ponraj, K.Annathurai, R.Kala

**Comments:** 8 Pages.

A graph with admits a k-remainder cordial labeling is called a k-remainder cordial graph. In this paper we investigate the 4- remainder cordial behavior of grid, subdivision of crown, Subdivision of bistar, book, Jelly fish, subdivision of Jelly fish, Mongolian tent graphs.

**Category:** General Mathematics

[68] **viXra:1809.0426 [pdf]**
*submitted on 2018-09-20 00:19:51*

**Authors:** B.Basavanagoud, Sujata Timmanaikar

**Comments:** 10 Pages.

All graphs considered here are finite, nontrivial, undirected with no loops and multiple edges. For graph theoretic terminology we refer to Harary.

**Category:** General Mathematics

[67] **viXra:1809.0425 [pdf]**
*submitted on 2018-09-20 00:20:53*

**Authors:** Qiuhui Mo, Xiangui Zhao, Qingnian Pan

**Comments:** 7 Pages.

In this paper, we study nonassociative algebras which satisfy the following identities:
(xy)z = (yx)z,x(yz) = x(zy).

**Category:** General Mathematics

[66] **viXra:1809.0424 [pdf]**
*submitted on 2018-09-20 00:22:12*

**Authors:** Rajesh Kumar T.J, Mathew Varkey T.K

**Comments:** 7 Pages.

Graph labeling where vertices and edges are assigned values subject to certain conditions have been motivated by various applied mathematical fields. Most of the problems
in graph labeling are discussed on undirected graphs. Bloom G.S. and Hsu D.F. defined the
labeling on directed graphs. In this paper, we discuss the adjacency matrices of graceful
digraphs such as unidirectional paths,alternating paths,many orientations of directed star and a class of directed bistar. We also discuss the adjacency matrices of unidirectional paths and alternating paths if they are odd digraceful.

**Category:** General Mathematics

[65] **viXra:1809.0423 [pdf]**
*submitted on 2018-09-20 00:23:18*

**Authors:** K.Pattabiraman

**Comments:** 13 Pages.

In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of strong product of a connected graph.

**Category:** General Mathematics

[64] **viXra:1809.0422 [pdf]**
*submitted on 2018-09-20 00:24:23*

**Authors:** B.O.Onasanya

**Comments:** 8 Pages.

In classical group theory, two elements composed yield another element. This theory, definitely, has limitations in its use in the study of atomic reactions and reproduction in organisms where two elements composed can yield more than one. In this paper, we partly give a review of some properties of hyperstructures with some examples in chemical
sciences.

**Category:** General Mathematics

[63] **viXra:1809.0421 [pdf]**
*submitted on 2018-09-20 00:25:31*

**Authors:** Barnali Laha, Arindam Bhattacharyya

**Comments:** 13 Pages.

Connected almost contact metric manifold was classified by S.Tanno, as those automorphism
group has maximum dimension.

**Category:** General Mathematics

[62] **viXra:1809.0420 [pdf]**
*submitted on 2018-09-20 00:26:30*

**Authors:** M. Subramanian, T. Subramanian

**Comments:** 13 Pages.

A graph G is said to be triple connected if any three vertices lie on a path in G. A dominating set S of a connected graph G is said to be a triple connected dominating set of G if the induced subgraph hSi is triple connected.

**Category:** General Mathematics

[61] **viXra:1809.0419 [pdf]**
*submitted on 2018-09-20 00:44:12*

**Authors:** P.K.Ashraf, K.A.Germina, N.K.Sudev

**Comments:** 7 Pages.

FIn this paper, we define the notion of set-valuations of signed graphs and discuss certain properties of signed graphs which admits certain types of set-valuations.

**Category:** General Mathematics

[60] **viXra:1809.0418 [pdf]**
*submitted on 2018-09-20 00:45:18*

**Authors:** O.P.Pandey, H.S.Shukla

**Comments:** 14 Pages.

We have obtained that due to this change of Finsler metric, the imbedding class of their tangent Riemannian space is increased at the most by two.

**Category:** General Mathematics

[59] **viXra:1809.0417 [pdf]**
*submitted on 2018-09-20 00:47:06*

**Authors:** I. Keerthi Asir, S. Athisayanathan

**Comments:** 17 Pages.

In 2011, Santhakumaran and Titus introduced and studied the concepts of monophonic distance in graphs.

**Category:** General Mathematics

[58] **viXra:1809.0416 [pdf]**
*submitted on 2018-09-20 00:48:09*

**Authors:** Abbas Alilou

**Comments:** 7 Pages.

A simple graph is a pair G = (V,E), where V = V (G) and E = E(G) are the sets of vertices and edges of G, respectively. A walk is an alternating sequence of vertices and connecting edges. A path is a walk that does not include any vertex twice, except that its first vertex might be the same as its last.

**Category:** General Mathematics

[57] **viXra:1809.0415 [pdf]**
*submitted on 2018-09-20 00:49:00*

**Authors:** E. M. Badr, B. Mohamed

**Comments:** 15 Pages.

In this paper we prove that the number of spanning trees of the linear and general cyclic snake networks is the same using the combinatorial approach.

**Category:** General Mathematics

[56] **viXra:1809.0414 [pdf]**
*submitted on 2018-09-20 00:50:00*

**Authors:** U M Prajapati, R M Gajjar

**Comments:** 16 Pages.

We begin with simple, finite, undirected graph G = (V (G),E(G)) where V (G) and E(G) denotes the vertex set and the edge set respectively.

**Category:** General Mathematics

[55] **viXra:1809.0413 [pdf]**
*submitted on 2018-09-20 00:51:06*

**Authors:** P.A. Ejegwa, A. M. Ibrahim

**Comments:** 18 Pages.

This paper proposes the concept of direct product of multigroups and its generalization.Some results are obtained with reference to root sets and cuts of multigroups.We prove that the direct product of multigroups is a multigroup. Finally, we introduce the notion of homomorphism and explore some of its properties in the context of direct product of multigroups and its generalization.

**Category:** General Mathematics

[54] **viXra:1809.0412 [pdf]**
*submitted on 2018-09-20 00:53:25*

**Authors:** T.Chalapathi, R.V M S S Kiran Kumar

**Comments:** 11 Pages.

This paper introduces equal degree graphs of simple existed graphs. These graphs exhibited some properties which are co-related with the older one. We characterize graphs for which their equal degree graphs are connected, completed, disconnected but not totally disconnected. We also obtain several properties of equal degree graphs and specify which graphs are isomorphic to equal degree graphs and complement of equal degree graphs. Furthermore, the relation between equal degree graphs and degree Prime graphs is determined.

**Category:** General Mathematics

[53] **viXra:1809.0411 [pdf]**
*submitted on 2018-09-20 00:54:24*

**Authors:** K.Praveena, M.Venkatachalam

**Comments:** 9 Pages.

An equitable k-coloring of a graph G is a proper k-coloring of G such that the sizes of any two color class differ by at most one.

**Category:** General Mathematics

[52] **viXra:1809.0410 [pdf]**
*submitted on 2018-09-20 00:55:12*

**Authors:** K. Muthugurupackiam, S.Ramya

**Comments:** 8 Pages.

A new graph characteristic, even modular edge irregularity strength of graphs is introduced. Estimation on this parameter is obtained and the precise values of this parameter are obtained for some families of graphs.

**Category:** General Mathematics

[51] **viXra:1809.0409 [pdf]**
*submitted on 2018-09-20 00:56:02*

**Authors:** Venkatesha, H.Aruna Kumara, R.T.Naveen Kumar

**Comments:** 10 Pages.

In this paper certain results on N(k)-contact metric manifold endowed with a extended quasi conformal curvature tensor are formulated.

**Category:** General Mathematics

[50] **viXra:1809.0408 [pdf]**
*submitted on 2018-09-20 00:56:57*

**Authors:** Gauree Shanker, Ramdayal Singh Kushwaha

**Comments:** 7 Pages.

In the present paper we have studied the Finslerian hypersurfaces and quartic change of a Finsler metric. The relationship with Finslerian hypersurface and the other which is finslerian hypersurface given by quartic change have been obtained. We have also proved that quartic change makes three type of hyper surfaces invarient under certain condition. These three type of hyper surfaces are hyperplanes of first, second, and third kind.

**Category:** General Mathematics

[49] **viXra:1809.0407 [pdf]**
*submitted on 2018-09-20 00:57:40*

**Authors:** N.Hosseinzadeh

**Comments:** 5 Pages.

We know that some large graphs can be constructed from some smaller graphs by using graphs operations. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this paper we investigate some operations of zero-divisor graph of posets.

**Category:** General Mathematics

[48] **viXra:1809.0406 [pdf]**
*submitted on 2018-09-20 00:58:42*

**Authors:** Linfan MAO

**Comments:** 27 Pages.

The main purpose of this paper is to extend Banach or Hilbert spaces to Banach or Hilbert continuity flow spaces over topological graphs and establish differentials on continuity flows for characterizing their globally change rate.

**Category:** General Mathematics

[47] **viXra:1809.0405 [pdf]**
*submitted on 2018-09-20 00:59:46*

**Authors:** Shouvik Datta Choudhury, Santu Dey, Arindam Bhattacharyya

**Comments:** 7 Pages.

Homology classes were first defined rigorously by Henri Poincar´e in his seminal paper “Analysis
situs” in 1895 referring to the work of Riemann,Betti and von Dyck. The homology group was
further developed by Emmy Noether and, independently, by Leopold Vietoris and Walther
Mayer in the period 1925-28.

**Category:** General Mathematics

[46] **viXra:1809.0404 [pdf]**
*submitted on 2018-09-20 01:13:42*

**Authors:** Handan Oztekin, Sezin Aykurt Sepet

**Comments:** 9 Pages.

In this study, we investigate a general intrinsic geometry in 3-dimensional Galilean space G3. Then, we obtain some special equations by using intrinsic derivatives of orthonormal triad in G3.

**Category:** General Mathematics

[45] **viXra:1809.0403 [pdf]**
*submitted on 2018-09-20 01:14:34*

**Authors:** A. Lourdusamy, Sherry George

**Comments:** 18 Pages.

The graphs considered here will be finite, undirected and simple. The symbols V(G) and E(G)
will denote the vertex set and edge set of a graph G respectively. p and q denote the number
of vertices and edges of G respectively.

**Category:** General Mathematics

[44] **viXra:1809.0402 [pdf]**
*submitted on 2018-09-20 01:15:42*

**Authors:** W.Barbara

**Comments:** 3 Pages.

The president of Academy of Mathematical Combinatorics with Applications (AMCA), Linfan Mao PhD won the Albert Nelson Marquis
Lifetime Achievement Award and has been endorsed by Marquis Who’s Who as a leader in the fields of mathematics and engineering, which was acknowledged by the notification of Marquis Who’s Who to Dr.Mao in June 26, 2017 and then the released in September 30, 2017.

**Category:** General Mathematics

[43] **viXra:1809.0401 [pdf]**
*submitted on 2018-09-20 01:16:53*

**Authors:** P.Siva Kota Reddy, K.N.Prakasha, Gavirangaiah K.

**Comments:** 10 Pages.

The concept of graph energy originates from chemistry to estimate the total π-electron
energy of a molecule. In chemistry the conjugated hydrocarbons can be represented by a graph
called molecular graph.

**Category:** General Mathematics

[42] **viXra:1809.0400 [pdf]**
*submitted on 2018-09-20 01:18:58*

**Authors:** Rajendra P., R.Rangarajan

**Comments:** 10 Pages.

Let G be a graph with vertex set V (G).

**Category:** General Mathematics

[41] **viXra:1809.0399 [pdf]**
*submitted on 2018-09-20 01:19:51*

**Authors:** P.Siva Kota Reddy, K.N.Prakasha, Gavirangaiah K.

**Comments:** 9 Pages.

In this paper, we introduce the minimum equitable dominating Randic energy of a graph and computed the minimum dominating Randic energy of graph. Also, established the upper and lower bounds for the minimum equitable dominating Randic energy of a graph.

**Category:** General Mathematics

[40] **viXra:1809.0398 [pdf]**
*submitted on 2018-09-20 01:20:56*

**Authors:** A. D Akwu, O. Oyewumi

**Comments:** 8 Pages.

In this article, we give the minimum number of moves required for the motion planning problem in Lexicographic products of some graphs. In addition,we proved the necessary and sufficient condition for the connectivity of the lexicographic product of two graphs.

**Category:** General Mathematics

[39] **viXra:1809.0397 [pdf]**
*submitted on 2018-09-20 01:30:34*

**Authors:** Brijesh Kumar Tripathi

**Comments:** 7 Pages.

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler (α, β) metrics.

**Category:** General Mathematics

[38] **viXra:1809.0396 [pdf]**
*submitted on 2018-09-20 01:31:42*

**Authors:** T.Deepa, M. Venkatachalam

**Comments:** 17 Pages.

In this paper we investigate the r-dynamic chromatic number of the central graph, middle graph, total graph and line graph of the triple star graph.

**Category:** General Mathematics

[37] **viXra:1809.0395 [pdf]**
*submitted on 2018-09-20 01:33:23*

**Authors:** N.R.Santhi Maheswari, C. Sekar

**Comments:** 12 Pages.

In 1965, Lofti A. Zadeh introduced the concept of fuzzy subset of a set as method of representing the phenomena of uncertainty in real life situation. K.T.Attanassov introduced
the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. K.T.Atanassov added
a new component( which determines the degree of non-membership) in the definition of fuzzy
set.

**Category:** General Mathematics

[36] **viXra:1809.0394 [pdf]**
*submitted on 2018-09-20 01:34:18*

**Authors:** Harishchandra S.Ramane, Gouramma A.Gudodagi, Raju B.Jummannaver

**Comments:** 24 Pages.

In this paper we obtain the terminal Hosoya polynomial for caterpillers, thorn stars and thorn
rings. These results generalizes the existing results.

**Category:** General Mathematics

[35] **viXra:1809.0393 [pdf]**
*submitted on 2018-09-20 01:35:35*

**Authors:** Akram Alqesmah, Anwar Alwardi, R. Rangarajan

**Comments:** 11 Pages.

In this paper, we introduce the first and second distance eccentricity Zagreb indices of a connected graph G as the sum of the squares of the distance eccentricity degrees of the vertices, and the sum of the products of the distance eccentricity degrees of pairs of adjacent vertices, respectively. Exact values for
some families of graphs and graph operations are obtained.

**Category:** General Mathematics

[34] **viXra:1809.0392 [pdf]**
*submitted on 2018-09-20 01:37:13*

**Authors:** B. Basavanagoud, Chitra E.

**Comments:** 23 Pages.

For a graph G, the first, second and third leap Zagreb indices are the sum of squares of 2-distance degree of vertices of G; the sum of product of 2-distance degree of end vertices of edges in G and the sum of product of 1-distance degree and 2-distance degrees of vertices of G, respectively.

**Category:** General Mathematics

[33] **viXra:1809.0391 [pdf]**
*submitted on 2018-09-20 01:39:05*

**Authors:** Seyda Kılıcoglu, Suleyman Senyurt, Abdussamet Calıskan

**Comments:** 11 Pages.

We give the striction curves of all Frenet ruled surfaces. Then the striction curves of involute and Bertrandian Frenet ruled surfaces are given in terms of the Frenet apparatus of the curve alpha.

**Category:** General Mathematics

[32] **viXra:1809.0390 [pdf]**
*submitted on 2018-09-20 01:40:08*

**Authors:** V. Lokesha, T. Deepika

**Comments:** 6 Pages.

In this paper, we discussed the Topological indices viz., Wiener, Harmonic, Geometric-Arithmetic(GA), first and second Zagreb indices of n-wheel graphs with bridges using operator techniques.

**Category:** General Mathematics

[31] **viXra:1809.0389 [pdf]**
*submitted on 2018-09-20 01:40:57*

**Authors:** F. Smarandache

**Comments:** 3 Pages.

Papers Published in IJMC, 2017

**Category:** General Mathematics

[30] **viXra:1809.0388 [pdf]**
*submitted on 2018-09-20 01:41:46*

**Authors:** A. Nellai Murugan, P. Iyadurai Selvaraj

**Comments:** 6 Pages.

A graph G is a finite non-empty set of objects called vertices together with a set of unordered
pairs of distinct vertices of G which is called edges.

**Category:** General Mathematics

[29] **viXra:1809.0387 [pdf]**
*submitted on 2018-09-20 01:42:43*

**Authors:** Ujwala Deshmukh, Smita A. Bhatavadekar

**Comments:** 6 Pages.

The graph that admits a prime labeling is said to be prime. G. Sethuraman has introduced concept of supersubdivision of a graph. In the light of this
concept, we have proved that supersubdivision by K2,2 of star, cycle and ladder are prime.

**Category:** General Mathematics

[28] **viXra:1809.0386 [pdf]**
*submitted on 2018-09-20 01:43:44*

**Authors:** Tamalika Dutta, Arindam Bhattacharyya

**Comments:** 12 Pages.

In this paper we have studied quasi conformal curvature tensor, Ricci tensor, projective curvature tensor, pseudo projective curvature tensor in Lorentzian Beta-Kenmotsu manifold admitting Ricci soliton and conformal Ricci soliton.

**Category:** General Mathematics

[27] **viXra:1809.0385 [pdf]**
*submitted on 2018-09-20 01:44:39*

**Authors:** V. Lokesha, P. S. Hemavathi, S. Vijay

**Comments:** 7 Pages.

In this paper we introduced the new notions semifull signed graph and semifull line (block) signed graph of a signed graph and its properties are obtained. Also, we obtained the structural characterizations of these notions. Further, we presented some switching equivalent characterizations.

**Category:** General Mathematics

[26] **viXra:1809.0384 [pdf]**
*submitted on 2018-09-20 01:45:32*

**Authors:** Siddesha M.S., Bagewadi C.S.

**Comments:** 12 Pages.

In this paper, we study the geometry of slant submanifolds of conformal (k, μ)-contact manifold when the tensor field Q is parallel. Further, we give a necessary and sufficient condition for a 3-dimensional slant submanifold of a 5-dimensional conformal (k, μ)-contact manifold to be a proper slant submanifold.

**Category:** General Mathematics

[25] **viXra:1809.0383 [pdf]**
*submitted on 2018-09-20 01:47:03*

**Authors:** Tanju Kahraman, Hasan Huseyin Ugurlu

**Comments:** 9 Pages.

In this paper, we consider the notion of the Smarandache curves by considering the asymptotic orthonormal frames of curves lying fully on lightlike cone in Minkowski 3-space R31.

**Category:** General Mathematics

[24] **viXra:1809.0382 [pdf]**
*submitted on 2018-09-20 01:47:55*

**Authors:** G.S.Saluja

**Comments:** 17 Pages.

In this paper, we establish some fixed point results for contractive type conditions in the framework of complete cone b-metric spaces and give some applications of our results. The results presented in this paper generalize, extend and unify several well-known comparable results in the existing literature.

**Category:** General Mathematics

[23] **viXra:1809.0381 [pdf]**
*submitted on 2018-09-20 01:49:15*

**Authors:** Deepak S. Revankar, Priyanka S. Hande, Satish P. Hande, Vijay Teli

**Comments:** 7 Pages.

The topological indices plays vital role in chemistry, pharmacology etc [1]. Let G = (V,E) be
a simple connected graph with vertex set.

**Category:** General Mathematics

[22] **viXra:1809.0380 [pdf]**
*submitted on 2018-09-20 01:50:09*

**Authors:** R.Ponraj, K.Annathurai, R.Kala

**Comments:** 11 Pages.

In this paper we investigate 4-prime cordial labeling behavior of shadow graph of a path, cycle, star, degree splitting graph of a bistar, jelly fish, splitting graph of a path and star.

**Category:** General Mathematics

[21] **viXra:1809.0379 [pdf]**
*submitted on 2018-09-20 01:51:08*

**Authors:** M. H. Akhbari, F. Movahedi, S. V. R. Kulli

**Comments:** 13 Pages.

In this paper, we obtain the domination number, the total domination number and the independent domination number in the neighborhood graph. We also investigate these parameters of domination on the join and the corona of two neighborhood graphs.

**Category:** General Mathematics

[20] **viXra:1809.0378 [pdf]**
*submitted on 2018-09-20 01:52:17*

**Authors:** H.S.Shukla, Neelam Mishra

**Comments:** 11 Pages.

We have studied quasi-C-reducibility, C-reducibility and semi-C-reducibility of the Finsler space with this metric. We have also calculated V-curvature tensor and T-tensor of the space with this changed metric in terms of v-curvature tensor and T-tensor respectively of the space with the original metric.

**Category:** General Mathematics

[19] **viXra:1809.0377 [pdf]**
*submitted on 2018-09-20 01:53:01*

**Authors:** Samir K. Vaidya, Raksha N. Mehta

**Comments:** 9 Pages.

In this paper we explore the concept of strong domination number and investigate strong domination number of some cycle related graphs.

**Category:** General Mathematics

[18] **viXra:1809.0376 [pdf]**
*submitted on 2018-09-20 01:54:14*

**Authors:** Hulya GULTEKINCITIL, Nihat ALTINISIK

**Comments:** 10 Pages.

In this paper, the eigenvalues and the eigenfunctions of the homogeneous fuzzy
Sturm-Liouville problem are examined under the three different situations according to the
boundary conditions. This examination is studied under the approach of Hukuhara differ-
entiability. The examples are given for this situations.

**Category:** General Mathematics

[17] **viXra:1809.0375 [pdf]**
*submitted on 2018-09-20 01:55:07*

**Authors:** Ahmed M. Naji, Soner Nandappa D

**Comments:** 12 Pages.

In this paper, we consider only simple graph G = (V,E), i.e., finite, having no loops no multiple
and directed edges. A graph G is said to be connected if there is a path between every pair of its vertices.

**Category:** General Mathematics

[16] **viXra:1809.0230 [pdf]**
*submitted on 2018-09-12 02:51:37*

**Authors:** Chaitali Kar, Bappa Mondal, Tapan Kumar Roy

**Comments:** 17 Pages.

In this paper, an inventory model is developed without shortages where the production cost is inversely related to the set up cost and production quantity. In addition, the holding cost is considered time dependent. Here impreciseness is introduced in the storage area. The objective and constraint functions are defined by the truth (membership) degree, indeterminacy (hesitation) degree and falsity (non-membership) degree. Likewise, a non-linear programming problem with a constraint is also considered.

**Category:** General Mathematics

[15] **viXra:1809.0229 [pdf]**
*submitted on 2018-09-12 02:53:15*

**Authors:** Shyamal Dalapati, Surapati Pramanik

**Comments:** 11 Pages.

Multi attribute group decision making with VIKOR (VlseKriterijuska Optimizacija I Komoromisno Resenje) strategy has been widely applied to solving real-world problems. Recently, Pramianik et al. [S. Pramanik, S. Dalapati, S. Alam, and T. K. Roy. NCVIKOR based MAGDM strategy under neutrosophic cubic set environment, Neutrosophic Sets and Systems, 20 (2018), 95-108]proposed VIKOR strategy for solving MAGDM, where compromise solutions are not identified in neutrosophic cubic environment. To overcome the shortcomings of the paper, we further modify the VIKOR strategy by incorporating compromise solution in neutrosophic cubic set environment. Finally, we solve an MAGDM problem using the modified NC-VIKOR strategy to show the feasibility,
applicability and effectiveness of the proposed strategy. Further, we present sensitivity analysis to show the impact of different values
of the decision making mechanism coefficient on ranking order of the alternatives.

**Category:** General Mathematics

[14] **viXra:1809.0228 [pdf]**
*submitted on 2018-09-12 03:02:12*

**Authors:** Surapati Pramanik, Partha Pratim Dey

**Comments:** 12 Pages.

The paper presents a novel strategy for solving bi-level linear programming problem based on goal programming in neutrosophic numbers environment. Bi-level linear programming problem comprises of two levels namely upper or first level and lower or second level with one objective at each level. The objective function of each level decision maker and the system
constraints are considered as linear functions with neutrosophic numbers of the form [p + q I], where p, q are real numbers and I represents indeterminacy.

**Category:** General Mathematics

[13] **viXra:1809.0227 [pdf]**
*submitted on 2018-09-12 03:03:19*

**Authors:** Nguyen Xuan Thao, Florentin Smarandache

**Comments:** 11 Pages.

In this paper, we first propose the concept of divergence measure on neutrosophic sets. We also provide some formulas for the divergence measure for neutrosophic sets. After that, we investigate the properties of proposed neutrosophic divergence measure. Finally, we also apply these formulas in medical problem and the classification problem.

**Category:** General Mathematics

[12] **viXra:1809.0226 [pdf]**
*submitted on 2018-09-12 03:04:38*

**Authors:** Fatimah M. Mohammed, Shaymaa F. Matar

**Comments:** 10 Pages.

In this paper, we state a new class of sets and called them fuzzy neutrosophic Alpham-closed sets, and we prove some theorem related to this definition. Then, we investigate the relation between fuzzy neutrosophic Alpham-closed sets, fuzzy neutrosophic α closed sets, fuzzy neutrosophic closed sets, fuzzy neutrosophic semi closed sets and fuzzy neutrosophic pre closed sets. On the other hand, some properties of the fuzzy neutrosophic Alpham-closed set are given.

**Category:** General Mathematics

[11] **viXra:1809.0225 [pdf]**
*submitted on 2018-09-12 03:05:42*

**Authors:** Sahidul Islam, Partha Ray

**Comments:** 10 Pages.

In this paper, we first consider a multi-objective Portfolio Selection model and then we add another entropy objective function and next we generalized the model. We solve the problems using Neutrosophic optimization technique. The models are illustrated with numerical examples.

**Category:** General Mathematics

[10] **viXra:1809.0224 [pdf]**
*submitted on 2018-09-12 03:06:52*

**Authors:** A. A. Salama, Florentin Smarandache, Hewayda ElGhawalby

**Comments:** 7 Pages.

In this paper, we propose a new technique for the enhancing images. It will work on removing the noise contained in the image as well as improving its contrast based on three different enhancing transforms, we commence by embedding the image into a neutrosophic domain; where the image will be mapped in three different levels, a level of trueness, a level of falseness
and a level of indeterminacy. Hence, we act separately on each level using the enhancement transforms. Finally, we introduce a new analysis in the field of analysis and processing of images using the neutrosophic crisp set theory via Mat lab program where has been obtained three images, which helps in a new analysis to improve and retrieve images.

**Category:** General Mathematics

[9] **viXra:1809.0223 [pdf]**
*submitted on 2018-09-12 03:07:51*

**Authors:** Riad Khidr Al-Hamido

**Comments:** 8 Pages.

In this paper, neutrosophic crisp bi-topological spaces, new types of open and closed sets in neutrosophic crisp bitopological spaces, the closure and interior neutrosophic crisp set and a new concept of open and closed sets are introduced. The basic properties of these types of open and closed sets and their properties are studied.

**Category:** General Mathematics

[8] **viXra:1809.0222 [pdf]**
*submitted on 2018-09-12 03:08:53*

**Authors:** Mehmet Şahin, Abdullah Kargın

**Comments:** 8 Pages.

In this article, a notion of neutrosophic triplet (NT) normed ring space is given and properties of NT normed ring spaces are studied. We demonstrate that NT normed ring is different from the classical one. Also, we show that a neutrosophic
triplet normed ring can be a neutrosophic triplet norm when certain conditions are met.

**Category:** General Mathematics

[7] **viXra:1809.0221 [pdf]**
*submitted on 2018-09-12 03:10:00*

**Authors:** T. Chalapathi, R. V. M. S. S. Kiran Kumar

**Comments:** 8 Pages.

In recent years, the inter connection between classical structures and Neutrosophic structures is studied by few researchers. For such kind of study, researchers defined new algebraic structures whose elements aregenerated by elements in classical algebraic set and indeterminate of the real world problem with respect to algebraic operations on the well defined Neutrosophic elements.

**Category:** General Mathematics

[6] **viXra:1809.0220 [pdf]**
*submitted on 2018-09-12 03:12:48*

**Authors:** Riad K. Al-Hamido, Qays Hatem Imran, Karem A. Alghurabi, Taleb Gharibah

**Comments:** 8 Pages.

In this paper, we presented another concept of neutrosophic crisp generalized closed sets called neutrosophic crisp semi-alpha-closed sets and studied their fundamental properties in neutrosophic crisp topological spaces.

**Category:** General Mathematics

[5] **viXra:1809.0219 [pdf]**
*submitted on 2018-09-12 03:17:21*

**Authors:** Ramona Parraga Alava, José Muñoz Murillo, Roy Barre Zambrano, María Isabel Zambrano Vélez, Maikel Leyva Vázquez

**Comments:** 9 Pages.

Neutrosophic cognitive maps and its application in decision making have become a topic of great importance for researchers and practitioners alike.PEST (Political, Economic, Social and Technological), analysis is a precondition analysis with the main functions of the identification of the environment within which and organization or project the operates and pr
viding data and information for enabling the organization to make predictions about new situations and circumstances.

**Category:** General Mathematics

[4] **viXra:1809.0218 [pdf]**
*submitted on 2018-09-12 03:18:18*

**Authors:** Florentin Smarandache

**Comments:** 14 Pages.

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some
given criteria.

**Category:** General Mathematics

[3] **viXra:1809.0217 [pdf]**
*submitted on 2018-09-12 03:19:20*

**Authors:** Suriana Alias, Daud Mohamad, Adibah Shuib

**Comments:** 20 Pages.

The concepts of rough neutrosophic multisets can be easily extended to a relation, mainly since a relation is also a set, i.e. a subset of a Cartesian product. Therefore, the objective of this paper is to define the definition of rough
neutrosophic multisets relation of Cartesian product over a universal set.

**Category:** General Mathematics

[2] **viXra:1809.0216 [pdf]**
*submitted on 2018-09-12 03:20:37*

**Authors:** Milton Villegas Alava, Stella Paola Delgado Figueroa, Hilda Mercedes Blum Alcivar, Maikel Leyva Vázquez

**Comments:** 9 Pages.

Neutrosophic sets and its application to decision support have become a topic of great importance. In this paper, a new model for decision making in the selection of projects is presented based on single valued neutrosophic number (SVNnumbers) and the analytic hierarchy process (AHP). The proposed framework is composed of five activities, framework, criteria weighting, gathering information, rating alternatives and project selection. Project alternatives are rated based on aggregation operator and the ranking of alternatives is based on scoring and accuracy functions.

**Category:** General Mathematics

[1] **viXra:1809.0009 [pdf]**
*submitted on 2018-09-01 03:51:18*

**Authors:** Han Geurdes

**Comments:** 4 Pages.

With the use of the even/odd number analysis it was found that there is no non-Goldbach even integer >4 number possible.

**Category:** General Mathematics