Graphs with large generalized (edge-)connectivity

Abstract

The generalized $k$-connectivity $\hat{I}{º}_k(G)$ 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 $\hat{I}{»}_k(G)$. In this paper, graphs of order $n$ such that $\hat{I}{º}_k(G)=n-\frac{k}{2}-1$ and $\hat{I}{»}_k(G)=n-\frac{k}{2}-1$ for even $k$ are characterized.

25 pages. arXiv admin note: text overlap with arXiv:1207.1838