Generalized (edge-)connectivity of join, corona and cluster graphs

The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a natural generalization of the classical connectivity. As a natural counterpart, Li et al. proposed the concept of generalized $k$-edge-connectivity $\lambda_k(G)$. In this paper, we obtain exact values or sharp upper and lower bounds of $\kappa_k(G)$ and $\lambda_k(G)$ for join, corona and cluster graphs