an:05543085
Zbl 1160.05039
Zhang, Lili; Hennayake, Kamal; Lai, Hong-Jian; Shao, Yehong
A lower bound of the \(l\)-edge-connectivity and optimal graphs
EN
J. Comb. Math. Comb. Comput. 66, 79-95 (2008).
00231666
2008
j
05C40 05C35
generalized edge connectivity; circulant graphs
Summary: For an integer \(l>1\), the \(l\)-edge-connectivity of a graph \(G\) with \(|V(G)| \geq l\), denoted by \(\lambda_l(G)\), is the smallest number of edges the removal of which results in a graph with \(l\) components. In this paper, we study lower bounds of \(\lambda_l(G)\) and optimal graphs that reach the lower bounds. Former results by \textit{F.T. Boesch} and \textit{S. Chen} [''A generalization of line connectivity and optimally invulnerable graphs,'' SIAM J. Math. 34, 657--665 (1978; Zbl 0386.05042)]are extended. We also present in this paper an optimal model of interconnection network \(G\) with a given \(\lambda_l(G)\) such that \(\lambda_2(G)\) is maximized while \(|E(G)|\) is minimized.
Zbl 0386.05042