Connectivity of Direct Products of Graphs

Details Connectivity of Direct Products of Graphs Connectivity of Direct Products of Graphs

2011-02-25

arxiv.org/abs/1102.5180v1

Mathematics

Combinatorics

5 pages, accepted by Ars Comb

Scientific paper

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.

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