Cyclic Vertex Connectivity of Trivalent Cayley Graphs

Abstract

A vertex subset F ⊆ V(G) is called a cyclic vertex-cut set of a connected graph G if G-F is disconnected such that at least two components in G-F contain cycles. The cyclic vertex connectivity is the cardinality of a minimum cyclic vertex-cut set. In this paper, we show that the cyclic vertex connectivity of the trivalent Cayley graphs TG_n is equal to eight for n ≥ 4.