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arXiv · 1705.08087

Two bounds for generalized $3$-connectivity of Cartesian product graphs

Hui Gao·Benjian Lv·Kaishun Wang
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Abstract

The generalized $k$-connectivity $κ_{k}(G)$ of a graph $G$, which was introduced by Chartrand et al.(1984) is a generalization of the concept of vertex connectivity. Let $G$ and $H$ be nontrivial connected graphs. Recently, Li et al. gave a lower bound for the generalized $3$-connectivity of the Cartesian product graph $G \square H$ and proposed a conjecture for the case that $H$ is $3$-connected. In this paper, we give two different forms of lower bounds for the generalized $3$-connectivity of Cartesian product graphs. The first lower bound is stronger than theirs, and the second confirms their conjecture.

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Hui Gao, Benjian Lv, Kaishun Wang. 2017-05-23. Two bounds for generalized $3$-connectivity of Cartesian product graphs. https://arxiv.org/abs/1705.08087

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