Graphs with large generalized (edge-)connectivity

The generalized $k$-connectivity $κ_k(G)$ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized $k$-edge-connectivity $λ_k(G)$. In this paper, graphs of order $n$ such that $κ_k(G)=n-\frac{k}{2}-1$ and $λ_k(G)=n-\frac{k}{2}-1$ for even $k$ are characterized.

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