Li, Xueliang and Mao, Yaping - The generalized 3-connectivity of Lexicographic product graphs

dmtcs:1266 - Discrete Mathematics & Theoretical Computer Science, June 2, 2014, Vol. 16 no. 1
The generalized 3-connectivity of Lexicographic product graphs

Authors: Li, Xueliang and Mao, Yaping

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
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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