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arXiv · 1708.05396

Sufficient conditions for graphs to be $k$-connected, maximally connected and super-connected

Zhen-Mu Hong·Zheng-Jiang Xia·Fuyuan Chen·Lutz Volkmann
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Abstract

Let $G$ be a connected graph with minimum degree $\delta(G)$ and vertex-connectivity $\kappa(G)$. The graph $G$ is $k$-connected if $\kappa(G)\geq k$, maximally connected if $\kappa(G) = \delta(G)$, and super-connected (or super-$\kappa$) if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is $k$-connected, maximally connected or super-connected if the number of edges or the spectral radius is large enough.

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Zhen-Mu Hong, Zheng-Jiang Xia, Fuyuan Chen, Lutz Volkmann. 2017-08-17. Sufficient conditions for graphs to be $k$-connected, maximally connected and super-connected. https://arxiv.org/abs/1708.05396

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