# Combinatorics and Graph Theory

## 1611 Submissions

[3] **viXra:1611.0385 [pdf]**
*submitted on 2016-11-28 14:44:16*

### New Lower Bounds for Van Der Waerden Numbers Using Genetic Algorithm

**Authors:** Alexey V. Komkov

**Comments:** Pages.

Genetic algorithm is a good tool for finding the global minimum in many discrete problems. In particular, it has proven itself in problems where there is no any apriori information about the possibilities of narrowing the search, or the specifics of the problem do not involve such. This work describes the procedure of using a genetic algorithm as applied to the search of van der Waerden numbers. Some new lower bounds of van der Waerden numbers were found using this procedure.

**Category:** Combinatorics and Graph Theory

[2] **viXra:1611.0327 [pdf]**
*submitted on 2016-11-23 16:16:31*

### A Neutrosophic Graph Similarity Measures

**Authors:** Shimaa Fathi, Hewayda Elghawalby, A.a. Salama

**Comments:** 8 Pages.

This paper is devoted for presenting new neutrosophic similarity measures between
neutrosophic graphs. We proposetwo ways to determine the neutrosophic distance between
neutrosophic vertex graphs. The two neutrosophic distances are based on the Haussdorff distance,and a robust modified variant of the Haussdorff distance, moreover we show that they both satisfy the metric distance measure axioms. Furthermore, a similarity measure between neutrosophic edge graphs that is based on a probabilistic variant of Haussdorff distance is introduced. The aim is to use those measures for the purpose of matching neutrosophic graphs whose structure can be described in the neutrosophic domain.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1611.0324 [pdf]**
*submitted on 2016-11-24 02:58:02*

### Foundation for Neutrosophic Mathematical Morphology

**Authors:** Eman.m.el-Nakeeb, H. Elghawalby, A.a.salama, S.a.el-Hafeez

**Comments:** 17 Pages.

The aim of this paper is to introduce a new approach to Mathematical Morphology based on
neutrosophic set theory. Basic definitions for neutrosophic morphological operations are extracted and a study of its algebraic properties is presented. In our work we demonstrate that neutrosophic morphological operations inherit properties and restrictions of Fuzzy Mathematical Morphology

**Category:** Combinatorics and Graph Theory