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Constructing edge-disjoint Steiner paths in lexicographic product networks

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  • Mao, Yaping

Abstract

Dirac showed that in a (k−1)-connected graph there is a path through each k vertices. The path k-connectivity πk(G) of a graph G, which is a generalization of Dirac’s notion, was introduced by Hager in 1986. It is natural to introduce the concept of path k-edge-connectivity ωk(G) of a graph G. Denote by G ○ H the lexicographic product of two graphs G and H. In this paper, we prove that ω3(G∘H)≥ω3(G)⌊3|V(H)|4⌋ for any two graphs G and H. Moreover, the bound is sharp. We also derive an upper bound of ω3(G ○ H), that is, ω3(G∘H)≤min{2ω3(G)|V(H)|2,δ(H)+δ(G)|V(H)|}. We demonstrate the usefulness of the proposed constructions by applying them to some instances of lexicographic product networks.

Suggested Citation

  • Mao, Yaping, 2017. "Constructing edge-disjoint Steiner paths in lexicographic product networks," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 1-10.
    • Handle: RePEc:eee:apmaco:v:308:y:2017:i:c:p:1-10
    DOI: 10.1016/j.amc.2017.03.015
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    References listed on IDEAS

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    1. Li, Shasha & Tu, Jianhua & Yu, Chenyan, 2016. "The generalized 3-connectivity of star graphs and bubble-sort graphs," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 41-46.
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