Cyclic vertex connectivity of star graphs

Authors:
Zhihua Yu;Qinghai Liu;Zhao Zhang
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China
Venue:
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Year:
2010

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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 SGn has κc(SGn) = 6(n - 3).