SHARP UPPER BOUNDS FOR GENERALIZED EDGE-CONNECTIVITY OF PRODUCT GRAPHS

The generalized k-connectivity K-k(G) of a graph G was introduced by Hager in 1985. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized k-edge-connectivity which is defined as lambda(k)(G) = min{lambda(S) : S subset of V(G) and vertical bar S vertical bar = k}, where lambda(S) denote the maximum number l of pairwise edge-disjoint trees T-1,T-2,...,T-l in G such that S subset of V(T-i) for 1 <= i <= l. In this paper, we study the generalized edge connectivity of product graphs and obtain sharp upper bounds for the generalized 3-edge-connectivity of Cartesian product graphs and strong product graphs. Among our results, some special cases are also discussed.