λc-Optimally half vertex transitive graphs with regularity k

  • Authors:

  • Yingzhi Tian;Jixiang Meng

  • Affiliations:

  • College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, Peoples Republic of China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, Peoples Republic of China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2009

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Abstract

The cyclic edge connectivity @l"c(G) of a graph G is the minimum number of edges whose removal results in a disconnected graph and every connected component contains cycles. If @l"c(G) exists, we call G@l"c-connected. And if @l"c(G) gets the maximum value, we call G@l"c-optimal. A bipartite graph is said to be half vertex transitive if its automorphism group is transitive on the sets of its bipartition. In this paper, we show that a connected k(=4)-regular half vertex transitive graph G with girth g=6 is @l"c-optimal, and we also obtain a sufficient and necessary condition for a connected k(=4)-regular half vertex transitive graph G with girth 4 to be @l"c-optimal.