Edge-connectivity and edge-superconnectivity in sequence graphs

Given an integer k >=, I and any graph G, the sequence graph S-k (G) is the graph whose set of vertices is the set of all walks of length k in G. Moreover, two vertices of S-k (G) are joined by an edge if and only if their corresponding walks are adjacent in G. In this paper we prove sufficient conditions for a sequence graph S-k (G) to be maximally edge-connected and edge-superconnected depending on the parity of k and on the vertex-connectivity of the original graph G. (C) 2007 Elsevier B.V. All rights reserved.