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...

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 ...

Let Λ(n) be the smallest number so that there are two n chromatic graphs whose product has chromatic number Λ(n). Under the assumption that a certain sharper result than one obtained by Duffus, Sands and Woodrow [1] holds we will prove that Λ(n) ≥ n/2. MR Subject Classifications [2000]: 05C15 Keyworks: chromatic number, graph product, Hedeniemi conjecture

The edge-bandwidth of a graph G is the bandwidth of the line graph of G. We show asymptotically tight bounds on the edge-bandwidth of two dimensional grids and tori, the product of two cliques and the n-dimensional hypercube.

We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of products of graphs.

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

We consider the question of computing the strong edge coloring, square graph coloring, and their generalization to coloring the k power of graphs. These problems have long been studied in discrete mathematics, and their “chaotic” behavior makes them interesting from an approximation algorithm perspective: For k = 1, it is well-known that vertex coloring is “hard” and edge coloring is “easy” in ...

Graph products have important role in constructing many useful networks. It is known that there are four basic graph products. Properties of each product have been studied individually. We propose a unified approach to these products based on the distance in graphs, and new two products on graphs. The viewpoint of products based on the distance introduced here provides a family of products that...

A graph product is the fundamental group of a graph of groups. Amongst the simplest examples are HNN groups and free products with amalgamation. The torsion and conjugacy theorems are proved for any group presented as a graph product. The graphs over which some graph product has a solvable word problem are characterised. Conditions are then given for the solvability of the word and order proble...