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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2014

The generalized 3-connectivity of Lexicographic product graphs

Abstract

The generalized k-connectivity κk(G) of a graph G, first introduced by Hager, is a natural generalization of the concept of (vertex-)connectivity. Denote by G^H and G&Box;H the lexicographic product and Cartesian product of two graphs G and H, respectively. In this paper, we prove that for any two connected graphs G and H, κ3(G^H)≥ κ3(G)|V(H)|. We also give upper bounds for κ3(G&Box; H) and κ3(G^H). Moreover, all the bounds are sharp.
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Dates and versions

hal-01179222 , version 1 (22-07-2015)

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Xueliang Li, Yaping Mao. The generalized 3-connectivity of Lexicographic product graphs. Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 1 (1), pp.339--353. ⟨10.46298/dmtcs.1266⟩. ⟨hal-01179222⟩

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