in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.

of my thesis In this work we are going to study two problems in graph theory and describe two parallel algorithms for solving them. The problem of finding a minimum spanning tree (MST) in a connected graph G = (V,E) with integer-valued edge weights, is the first problem we are going to study. We give a new deterministic parallel algorithm for computing the minimum spanning tree of a given graph...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

In this article, we explain how to calculate the adjacency matrix and the characteristic polynomial of a derived voltage graph when the voltage group is abelian as presented in [1]. We then present a theorem for calculating the adjacency matrix of a derived voltage graph for any voltage group, abelian or non-abelian.

The representatives formulation for the vertex coloring problem is revisited to remove symmetry and new versions of facets derived from substructures of the graph are presented. In addition, a new class of facets is derived from independent sets of the graph. Finally, a comparison with the independent sets formulation is provided.

Graphs are commonly used to encode relationships among entities, yet, their abstractness makes them incredibly difficult to analyze. Node-link diagrams are a popular method for drawing graphs. Classical techniques for the node-link diagrams include various layout methods that rely on derived information to position points, which often lack interactive exploration functionalities; and force-dire...

This paper derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via strong equivalence relation. We show that any weak single-valued neutrosophic graph is a derived single-valued neutrosophic graph and any linear weak single-valued neutrosophic tree is an extendable linear single-valued neutrosophic tree.

We prove a necessary and sufficient condition under which a connected graph has a connected P3-path graph. Moreover, an analogous condition for connectivity of the Pk-path graph of a connected graph which does not contain a cycle of length smaller than k+1 is derived.

The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎