Generalized 3-Connectivity and 3-Edge-Connectivity for the Cartesian Products of Some Graph Classes

Abstract

The generalized $k$-connectivity ${\kappa }_k(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized $k$-edge-connectivity. In this paper, we completely determine the precise values of the generalized $3$-connectivity and generalized $3$-edge-connectivity for the Cartesian products of some graph classes.