Connectivity of Direct Products of Graphs

Wei Wang; Ni-Ni Xue

Connectivity of Direct Products of Graphs

Combinatorics 2013-07-09 v1

Authors: Wei Wang , Ni-Ni Xue

Abstract

Let $\kappa(G)$ be the connectivity of $G$ and $G\times H$ the direct product of $G$ and $H$ . We prove that for any graphs $G$ and $K_n$ with $n\ge 3$ , $\kappa(G\times K_n)=min\{n\kappa(G),(n-1)\delta(G)\}$ , which was conjectured by Guji and Vumar.

Keywords

graph connectivity direct product complete graph Cartesian product graph theory

Cite

@article{arxiv.1102.5180,
  title  = {Connectivity of Direct Products of Graphs},
  author = {Wei Wang and Ni-Ni Xue},
  journal= {arXiv preprint arXiv:1102.5180},
  year   = {2013}
}

Comments

5 pages, accepted by Ars Comb

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