Conditional connectivity of Cayley graphs generated by transposition trees

Authors:
Weihua Yang;Hengzhe Li;Jixiang Meng
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR China and School of Mathematical Science, Xiamen University, Xiamen Fujian 361005, PR China;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
Venue:
Information Processing Letters
Year:
2010

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Abstract

Given a graph G and a non-negative integer h, the R"h-(edge)connectivity of G is the minimum cardinality of a set of (edges)vertices of G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least h. Similarly, given a non-negative integer g, the g-(edge)extraconnectivity of G is the minimum cardinality of a set of (edges)vertices of G, if any, whose deletion disconnects G, and every remaining component has more than g vertices. In this paper, we determine R"2-(edge)connectivity and 2-extra(edge)connectivity of Cayley graphs generated by transposition trees.