SOME RESULTS FOR THE RUPTURE DEGREE

Abstract

The rupture degree of an incomplete connected graph G is defined by[Formula: see text] where w(G − S) denotes the number of components in the graph G − S and m(G − S) is the order of the largest component of G − S. This parameter can be used to measure the vulnerability of a graph. In this paper, some bounds consisted of the relationships between the rupture degree and some vulnerability parameters on the rupture degree of a graph are given.