[3] **viXra:1807.0486 [pdf]**
*submitted on 2018-07-28 07:02:51*

**Authors:** Yair Lavi

**Comments:** 5 Pages.

We formulate conjectures regarding the maximum value and maximizing matrices
of the permanent and of diagonal products on the set of stochastic matrices with
bounded rank. We formulate equivalent conjectures on upper bounds for these func-
tions for nonnegative matrices based on their rank, row sums and column sums.
In particular we conjecture that the permanent of a singular nonnegative matrix is
bounded by 1/2 times the minimum of the product of its row sums and the product of
its column sums, and that the product of the elements of any diagonal of a singular
nonnegative matrix is bounded by 1/4 times the minimum of the product of its row
sums and the product of its column sums.

**Category:** Combinatorics and Graph Theory

[2] **viXra:1807.0384 [pdf]**
*replaced on 2018-07-25 16:31:37*

**Authors:** Marco Ripà, Valerio Bencini

**Comments:** 14 Pages.

In this paper we describe two new patterns, in order to improve the upper bound for the Ripà’s n X n X n points problem, saving a few lines for many values of n. The new upper bound, for any n≥6, becomes h_u(n)=int((3/2*n^2)+int(n/4)-int((n-1)/4)+int((n+1)/4)-int((n+2)/4)+n-2, where int(x)≔floor(x).

**Category:** Combinatorics and Graph Theory

[1] **viXra:1807.0114 [pdf]**
*submitted on 2018-07-04 09:45:17*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, V. Venkateswara Rao

**Comments:** 20 Pages. Neutrosophic Operational Research Volume III

The neutrosophic set theory, proposed by smarandache, can be used as a general mathematical tool for dealing with indeterminate and inconsistent information. By applying the concept of neutrosophic sets on graph theory, several studies of neutrosophic models have been presented in the literature. In this paper, the concept of complex neutrosophic graph of type 1 is extended to interval complex neutrosophic graph of type 1(ICNG1). We have proposed a representation of ICNG1 by adjacency matrix and studied some
properties related to this new structure. The concept of ICNG1 generalized the concept of generalized fuzzy graphs of type 1 (GFG1), generalized single valued neutrosophic graphs of type 1 (GSVNG1) generalized interval valued neutrosophic graphs of type 1 (GIVNG1) and complex neutrosophic graph type 1(CNG1).

**Category:** Combinatorics and Graph Theory