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

dmtcs:1266 - Discrete Mathematics & Theoretical Computer Science, June 2, 2014, Vol. 16 no. 1 - https://doi.org/10.46298/dmtcs.1266
The generalized 3-connectivity of Lexicographic product graphsArticle

Authors: Xueliang Li 1; Yaping Mao ORCID2

  • 1 Center for Combinatorics [Nankai]
  • 2 Department of Mathematics [Qianghai]

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.

Volume: Vol. 16 no. 1
Section: Graph Theory
Published on: June 2, 2014
Accepted on: July 23, 2015
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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