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

Hui Gao, Benjian Lv and Kaishun Wang

Applied Mathematics and Computation, 2018, vol. 338, issue C, 305-313

Abstract: The generalized k-connectivity κk(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. (2012) gave a lower bound for the generalized 3-connectivity of the Cartesian product graph G□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.

Keywords: Connectivity; Generalized connectivity; Cartesian product (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:338:y:2018:i:c:p:305-313

DOI: 10.1016/j.amc.2018.04.007

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