The connectivity of hierarchical Cayley digraphs (Q1199430)

Let \(S\) be a set of generators of a group \(G\). \(S\) is said to be hierarchical if there exists an ordering of \(S\) such that the subgroup \(S_ i\) generated by the first \(i\) elements of the ordering is a proper subgroup of \(S_{i+1}\). If \(S\) is hierarchical and \(S\subseteq\overline S\subseteq S\cup S^{-1}\) then the Cayley digraph on \(G\) and \(\overline S\) is said to be a hierarchical Cayley digraph (see \textit{S. B. Akers} and \textit{B. Krishnamurthy} [IEEE Trans. Comput. C-36, 885-888 (1987; Zbl 0641.94049)]). Here the authors show that hierarchical Cayley digraphs have maximum connectivity except some explicit defined cases in which the connectivity is one unit less.