A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs

The generalized $k$-connectivity $ \kappa_k (G) $ of a graph $G$, mentioned by Hager in 1985, is a natural generalization of the path-version of the classical connectivity. 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) = \text{min} \{ \lambda_G (S) | S \subseteq V (G) $ and $ |S| = k \} $, where $ \lambda_G (S) $ denote the maximum number $ \mathcal{l} $ of pairwise edge-disjoint trees $ T_1 $, $ T_2 $, . . ., $ T_\mathcal{l} $ in $G$ such that $S \subseteq V (T_i)$ for $ 1 \le i \le \mathcal{l} $. In this paper we get a sharp lower bound for the generalized 3-edge-connectivity of the strong product of any two connected graphs.