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.

Source : oai:HAL:hal-01179222v1

Volume: Vol. 16 no. 1 (in progress)

Section: Graph Theory

Published on: June 2, 2014

Submitted on: August 12, 2013

Keywords: Graph Theory, Discrete Mathematics, Theoretical Computer Science,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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