Vulnerability: Integrity of a middle graph

A communication network can be considered to be highly vulnerable to disruption if the destruction of a few elements can result in no member’s being able to communicate with very many others. This idea suggests the concept of the integrity of a graph. The vertex-integrity of a graph G, denoted I(G), is defined by I(G)= $ minatop{S subset V(G}$ where m(G-S) denotes the maximum order of a component of G-S. In this paper we consider the integrity of middle graphs of specific families of graphs and combinations of these graphs.A communication network can be considered to be highly vulnerable to disruption if the destruction of a few elements can result in no member’s being able to communicate with very many others. This idea suggests the concept of the integrity of a graph. The vertex-integrity of a graph G, denoted I(G), is defined by I(G)= $ minatop{S subset V(G}$ where m(G-S) denotes the maximum order of a component of G-S. In this paper we consider the integrity of middle graphs of specific families of graphs and combinations of these graphs