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Integrity of quasi-total graphs
B. Basavanagoud,P. Jakkannavar,I. N. Cangul 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.4
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) = minS⊂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.