Edge-connectivity and edge-superconnectivity in sequence graphs (Q2384389)

The vertex set of the sequence graph \(S_k(G)\) of a graph \(G\) is the set of all \(k\)-walks in \(G\), two vertices in \(S_k(G)\) are adjacent when corresponding walks are consecutive. Graph \(G\) is maximally edge-connected if the edge connectivity of \(G\) is equal to its minimum degree. A maximally edge-connected graph \(G\) is edge-superconnected if each minimum edge-cut consists of all edges incident with some vertex. In the paper are presented some sufficient conditions for the maximal edge-connectivity and edge-superconnectivity of sequence graphs.