Edge-connectivity and edge-superconnectivity in sequence graphs

Given an integer k⩾1k⩾1 and any graph GG, the sequence graph Sk(G)Sk(G) is the graph whose set of vertices is the set of all walks of length kk in GG. Moreover, two vertices of Sk(G)Sk(G) are joined by an edge if and only if their corresponding walks are adjacent in GG.In this paper we prove sufficient conditions for a sequence graph Sk(G)Sk(G) to be maximally edge-connected and edge-superconnected depending on the parity of kk and on the vertex-connectivity of the original graph GG.