The exponent of the strong product of a digraph of order m and a digraph of order n is shown to be bounded above by m+n− 2, with equality for Zm ⊠Zn. The exponent and diameter of the strong product of a graph and a digraph are also investigated.

We prove that the class of nontrivial connected strong product graphs is weakly reconstructible. We also show that any nontrivial connected thin strong product graph can be uniquely reconstructed from each of its one-vertex-deleted deleted subgraphs. © 2006 Elsevier B.V. All rights reserved. MSC: 05C

The exponent of the strong product of a digraph of order m and a digraph of order n is shown to be bounded above by m+n− 2, with equality for Zm ⊠Zn. The exponent and diameter of the strong product of a graph and a digraph are also investigated.

Let G = (V, E) be a graph. We define strong dominating color number of a graph G as the maximum number of color classes which are strong dominating sets of G, and is denoted by sd(G) , where the maximum is taken over all  -coloring of G. This paper determines the exact values of strong dominating color number of sum and Cartesian product of graphs.

In11, Kulli and Janakiram initiate the concept of maximal domination in graphs. In this paper, we obtained some bounds characterizations. Also, estimate value number graph products such as join graphs, corona product, cartesian product strong product.

Graph bundles generalize the notion of covering graphs and products of graphs. The chromatic numbers of product bundles with respect to the Cartesian, strong and tensor product whose base and fiber are cycles are determined.

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this ...

The multiplicative sum Zagreb index is defined for a simple graph G as the product of the terms dG(u)+dG(v) over all edges uv∈E(G) , where dG(u) denotes the degree of the vertex u of G . In this paper, we present some lower bounds for the multiplicative sum Zagreb index of several graph operations such as union, join, corona product, composition, direct product, Cartesian product and strong pro...