On weak hub-integrity of graphs

Abstract

The concept of weak hub-integrity is introduced as a new measure of the stability of a graph G and it is defined as WHI(G) = min{ |S| + m_e(G - S) }, where S is a hub set and m_e(G - S) denotes the number of edges in the largest component of G - S. In this paper, the weak hub-integrity of some graphs is obtained. The relations between weak hub-integrity and other parameters are determined. Also, some results connecting the weak hub-integrity and binary graph operations are established.