A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. A bipolar fuzzy graph structure is a generalization of a bipolar fuzzy graph. In this paper, we present several different types of operations, including composition, Cartesian product, strong product, cross product, and lexicographic product on ...

Abstract—In graph theory, different types of products of two graphs had been studied, e.g., Cartesian product, Tensor product, Strong product, etc. In this paper we generalize the concept of Cartesian product of graphs.We define 2 Cartesian product and more generally r Cartesian product of two graphs. We study these product mainly for path graphs. We also discuss connectedness of the new graph.

We present a Multiple Attribute Graph (MARG) Matching algorithm. The algorithm operates on a strong product graph, where vertices correspond to hypothesized matchings between two nodes and edges specify compatibilities between two matches. We show how the matching problem reduces to partitioning the strong product graph, which we solve with spectral clustering. We test our algorithm on a few im...

A tree T , in an edge-colored graph G, is called a rainbow tree if no two edges of T are assigned the same color. A k-rainbow coloring of G is an edge coloring of G having the property that for every set S of k vertices of G, there exists a rainbow tree T in G such that S ⊆ V (T ). The minimum number of colors needed in a k-rainbow coloring of G is the k-rainbow index of G, denoted by rxk(G). G...

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.

Suppose G = (V,E) is a graph and D = (V,F) is a strong orientation of G. Let u,v ∈ V, the strong distance sd(u,v) is the minimum size of strong subdigraph of D containing u and v, the strong eccentricity se(u) is the maximum strong distance sd(u,v) between u and v for all v ∈ V. The strong radius and strong diameter of D is defined as the minimum and maximum se(u) for all u ∈ V, respectively. A...

Recent work of Gromov, Epstein, Cannon, Thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups. (See [16],[17] and [14].) Many of these structures are preserved by taking graph products. The graph product of groups (not to be confused with the fundamental group of a graph of groups) is a product mixing direct and f...

The total irregularity of a graph G is defined as irrt .G/ D 1 2 P u;v2V.G/ jdG.u/ dG.v/j, where dG.u/ denotes the degree of a vertex u 2 V.G/. In this paper we give (sharp) upper bounds on the total irregularity of graphs under several graph operations including join, lexicographic product, Cartesian product, strong product, direct product, corona product, disjunction and symmetric difference....

The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑ uv∈E(G) |dG(u)− dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and symmetric difference. ...