On the Edge Connectivity of Direct Products with Dense Graphs |
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Authors: | Wei Wang Zhidan Yan |
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Institution: | 1. College of Information Engineering, Tarim University, Alar, 843300, China
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Abstract: | Let ${\kappa^{\prime}(G)}$ be the edge connectivity of G and G × H the direct product of G and H. Let H be any graph with minimal degree ${\delta(H)>|V(H)|/2}$ . We prove that for any graph ${G, \kappa^{\prime}(G\times H)=\textup{min}\{2\kappa^{\prime}(G)|E(H)|,\delta(G)\delta(H)\}}$ . In addition, the structure of minimum edge cuts is described. As an application, we present a necessary and sufficient condition for G × K n (n ≥ 3) to be super edge connected. |
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