SOME RESULTS FOR THE RUPTURE DEGREE

WOS: 000335513900009The rupture degree of an incomplete connected graph G is defined by r(G) = max{w(G - S) - vertical bar S vertical bar - m(G - S) : S CV(G), w(G - S) >= 2}, where w(G - 5) denotes the number of components in the graph G - S and m(G - 5) 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