A kind of conditional fault tolerance of alternating group graphs

  • Authors:
  • Zhao Zhang;Wei Xiong;Weihua Yang

  • Affiliations:
  • College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR China;School of Mathematical Science, Xiamen University, Xiamen, Fujian, 361005, PR China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2010

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Abstract

A vertex subset F is a k-restricted vertex-cut of a connected graph G if G-F is disconnected and every vertex in G-F has at least k good neighbors in G-F. The cardinality of the minimum k-restricted vertex-cut of G is the k-restricted connectivity of G, denoted by @k^k(G). This parameter measures a kind of conditional fault tolerance of networks. In this paper, we show that for the n-dimensional alternating group graph AG"n, @k^2(AG"4)=4 and @k^2(AG"n)=6n-18 for n=5.