On optimally-λ(3) transitive graphs

Authors:
Zhao Zhang;Jixiang Meng
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China and Department of Mathematics, Zhengzhou University, Henan, Zhengzhou, People's Republ ...;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

Let X = (V, E) be a connected graph and S ⊆ E. S is said to be an m-restricted edge cut if X - S is disconnected and each component of X - S contains at least m vertices. Let λ(m) (X) be the minimum size of all m-restricted edge cuts, and ξm(X) = min{ω(U): U ⊆ V, |U| = m and X[U] is connected }, where ω(U) is the number of edges with one end in U and the other end in V\U, X[U] is the subgraph of X induced by U. A graph X is said to be optimally-λ(3) if λ(i)(X) = ξi (X) (i = 1, 2, 3). In this paper, optimally-λ (3) vertex-transitive graphs are studied. In particular, generating sets of optimally-λ(3) minimal Cayley graphs are completely characterized.