On the Super Spanning Properties of Binary Wrapped Buttefly Graphs

Abstract

A k-container Ck(u; v) of a graph G is a set of k internally vertex-disjoint paths joining vertices u and v. It becomes a k*-container if every vertex of G is passed by a certain path of Ck(u; v). A graph G is said to be k*-connected if there exists a k*-container between any two vertices of G. A graph G with connectivity · is super spanning connected if it is i*-connected for every 1≦ i ≦k. A bipartite graph G is k*-laceable if there exists a k*-container between any two vertices u and v from different partite sets of G. A bipartite graph G with connectivity k is super spanning laceable if it is i*-laceable for all 1≦ i ≦k. In this paper, we show the n-dimensional binary wrapped butterfly graph is super spanning connected (resp. super spanning laceable) if n is odd (resp. even).