Reliability of interconnection networks modeled by a product of graphs

Abstract

The product graph G m * G p of two given graphs G m and This work deals with product graphs for which we provide bounds for the connectivity parameter κ. Moreover, we state sufficient conditions that guarantee these product graphs to be maximally connected or superconnected. As a consequence, we deduce that even small networks with low reliability may lead to larger networks with high levels of fault-tolerance.

On super connectivity of Cartesian product graphs

“…In Section 2 we recall some definitions and establish notation. Section 3 provides bounds for the super connectivity of Cartesian product graphs by refining the technique of Balbuena et al in [3]. In particular, we determine…”

Reliability of interconnection networks modeled by Cartesian product digraphs

“…We also note that Balbuena et al [1] defined the product graph G 1 × G 2 of two undirected graphs G 1 and G 2 , which is a generalization of both the Cartesian product graphs and the permutation graphs. Thus, it is interesting to determine the connectivity and edge-connectivity of G 1 × G 2 .…”

“…Balbuena et al [1] considered a generalization of the Cartesian product of graphs, the product graph G 1 × G 2 of two undirected graphs G 1 and G 2 , and obtained…”

“…Motivated by the technique in [1], in this note, we completely determine the connectivity and the edge-connectivity of the Cartesian product of two digraphs G 1 and G 2 as follows:…”

Fault diameter of product graphs

“…The product graph is a good method in constructing large graphs with given degree and diameter there and first proposed by Bermond et al in [3], in which the connectivity and diameter of G 1 * G 2 is discussed. In the paper by Balbuena et al [1], the connectivity of G 1 * G 2 is discussed deeper.…”