[8] **viXra:1604.0188 [pdf]**
*submitted on 2016-04-12 01:22:25*

**Authors:** Linfan Mao

**Comments:** 141 Pages.

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original researchpapers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.

**Category:** Combinatorics and Graph Theory

[7] **viXra:1604.0187 [pdf]**
*submitted on 2016-04-12 01:23:59*

**Authors:** B. Chaluvaraju, H.S. Boregowda, S. Kumbinarsaiah

**Comments:** 6 Pages.

The binding number of a graph G = (V,E) is deﬁned to be the minimum of |N(X)|/|X| taken over all nonempty set X ⊆ V (G) such that N(X) 6= V (G). In this article, we explore the properties and bounds on binding number of some special classes of trees.

**Category:** Combinatorics and Graph Theory

[6] **viXra:1604.0185 [pdf]**
*submitted on 2016-04-12 01:26:19*

**Authors:** Suleyman Senyurt, Abdussamet Calıskan, Unzile Celik

**Comments:** 7 Pages.

In this paper, let (α,α∗) be Bertrand curve pair, when the unit Darboux vector of the α∗ curve are taken as the position vectors, the curvature and the torsion of Smarandache curve are calculated. These values are expressed depending upon the α curve. Besides, we illustrate example of our main results.

**Category:** Combinatorics and Graph Theory

[5] **viXra:1604.0184 [pdf]**
*submitted on 2016-04-12 01:27:49*

**Authors:** Nutan G. Nayak

**Comments:** 8 Pages.

In this paper, we obtained the characterization of net-regular signed graphs and also established the spectrum for one class of heterogeneous unbalanced net-regular signed complete graphs.

**Category:** Combinatorics and Graph Theory

[4] **viXra:1604.0183 [pdf]**
*submitted on 2016-04-12 01:29:16*

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

**Comments:** 8 Pages.

A graph with a quotient cordial labeling is called a quotient cordial graph. We investigate the quotient cordial labeling behavior of path, cycle, complete graph, star, bistar etc.

**Category:** Combinatorics and Graph Theory

[3] **viXra:1604.0182 [pdf]**
*submitted on 2016-04-12 01:30:56*

**Authors:** Linfan MAO

**Comments:** 141 Pages.

The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences.

**Category:** Combinatorics and Graph Theory

[2] **viXra:1604.0111 [pdf]**
*replaced on 2016-05-07 19:06:06*

**Authors:** A. A. Frempong

**Comments:** 8 Pages. Copyright © by A. A. Frempong. Reference: P vs NP:Solutions of NP Problems,viXra:1408.0204 by A. A. Frempong

This paper covers the principles and procedures for producing the solution of a problem given the procedure for checking the solution of the problem and vice versa. If a problem can be checked in polynomial time, it can be solved in polynomial time, provided a complete checking procedure is available. From a point A, if one uses one's feet to measure a certain distance by counting steps forwards to a point B, and one wants to check the correctness of the measurement, one would count backwards from the point B using one's feet to see if one returns to exactly the point A. If one returns to A, the forward counting is correct, otherwise it is incorrect. If one counted backwards first from the point B to the point A, one could also count forwards from A to B. Before computers were used in filing taxes in the United States, when one prepared a tax return and wanted to check for arithmetic errors, one would reverse the arithmetic steps from the last arithmetic statement backwards all the way to the first entry on the tax form; and if one obtains a zero after reversing the steps, one was sure that there were no arithmetic errors on the tax form (That is, one began with zero entry going forward and one returned with a zero entry). So also, if one is able to check quickly and completely, the correctness of the solution to a problem, one should also be able to produce the solution of the problem by reversing the steps of the checking process while using opposite operations in each step. If a complete checking process is available, the solution process can be obtained by reversing the steps of the checking while using opposite operations in each step. In checking the correctness of the solution to a problem, one should produce the complete checking process which includes the end of the problem and the beginning of the problem. Checking only the final answer or statement is incomplete checking. Since the solution process and the checking process are inverses of each other, knowing one of them, one can obtain the other by reversing the steps while using opposite operations. To facilitate complete checking, the question should always be posed such that one is compelled to show a checking procedure from which the solution procedure can be deduced. Therefore P is always equal to NP.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1604.0012 [pdf]**
*submitted on 2016-04-02 01:31:57*

**Authors:** Ton Kloks, Jan van Leeuwen, Fu-Hong Liu, Hsiang-Hsuan Liu, Richard B. Tan, Yue-Li Wang

**Comments:** 12 Pages.

We show that the geodetic game is decidable in polynomial time for various classes of AT-free graphs.

**Category:** Combinatorics and Graph Theory