Weak reconstruction of strong product graphs

Weak reconstruction of strong product graphs

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

On the Weak Reconstruction of Strong Product Graphs

Generalized Degree Distance of Strong Product 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...

On the weak reconstruction of Cartesian-product graphs

In this paper we reconstruct nontrivial connected Cartesian product graphs from single vertex deleted subgraphs. We show that all one-vertex extensions of a given connected graph H, nite or innnite, to a nontrivial Cartesian product are isomorphic.

On global (strong) defensive alliances in some product graphs

A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one moreneighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The global defensive alliance number of a graph $G$ is the minimum cardinality of a global defensive alliance in $G$. In this article we study the global ...