CYCLIC CONNECTIVITY OF STAR GRAPH

Abstract

For a connected graph G, a vertex subset F ⊂ V(G) is a cyclic vertex-cut of G if G - F is disconnected and at least two of its components contain cycles. The cardinality of a minimum cyclic vertex-cut of G, denoted by κc(G), is the cyclic vertex-connectivity of G. In this paper, we show that for any integer n ≥ 4, the n-dimensional star graph SGnhas κc(SGn) = 6(n - 3).