Super Edge-Connectivity of Strong Product Graphs

Abstract

The super edge-connectivity [Formula: see text] of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G − F contains at least two vertices. Denote by [Formula: see text] the strong product of graphs G and H. For two graphs G and H, Yang proved that [Formula: see text]. In this paper, we give another proof of this result. In particular, we determine [Formula: see text] if [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the minimum edge-degree of a graph G.