A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

  • Authors:

  • Eddie Cheng;László Lipták;Weihua Yang;Zhao Zhang;Xiaofeng Guo

  • Affiliations:

  • Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, United States;Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, United States;School of Mathematical Science, Xiamen University, Xiamen, Fujian 361005, China;School of Mathematics, Xinjiang University, Urumqi 830046, China;School of Mathematical Science, Xiamen University, Xiamen, Fujian 361005, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

Let G be a graph. Then T@?V(G) is called an R^k-vertex-cut if G-T is disconnected and each vertex in V(G)-T has at least k neighbors in G-T. The size of a smallest R^k-vertex-cut is the R^k-vertex-connectivity of G and is denoted by @k^k(G). In this paper, we determine the numbers @k^1 and @k^2 for Cayley graphs generated by 2-trees, including the popular alternating group graphs.