Integrity of quasi-total graph

Abstract

A communication network can be considered to be highly vulnerable to dis¬ruption if the failure of few members 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 integrity I(G) of a graph G is defined as I(G) = min S⊂V(G) {|S| + m(G — S)} where m(G — S) denotes the order of the largest component of G — S. In this paper, we obtain the integrity of quasi-total graph of some standard graph families and combinations of these graphs. Further, we establish some relations connecting the integrity of some graph families and integrity of their quasi-total graphs.