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On strong Menger connectivity of (n,k)-bubble-sort networks

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  • Guo, Jia

Abstract

Let t≥0, r≥0 be two integers and G be a connected graph. Let S‾⊆V(G) and E‾⊆E(G) be any sets satisfying |S‾|≤t and |E‾|≤t. For any vertices u1, u2 of G−S‾ (resp. G−E‾) with u1≠u2, if G−S‾ (resp. G−E‾) has min{dG−S‾(u1),dG−S‾(u2)} (resp. min{dG−E‾(u1),dG−E‾(u2)}) vertex (resp. edge) disjoint paths connecting u1 and u2, then G is t-strongly Menger vertex (resp. edge) connected or briefly t-SMVC (resp. t-SMEC). If G is t-SMVC (resp. t-SMEC) for any set S‾ (resp. E‾) satisfying |S‾|≤t with δ(G−S‾)≥r (resp. |E‾|≤t with δ(G−E‾)≥r), then G is t-SMVC (resp. t-SMEC) of order r. We show that (n,k)-bubble-sort network Bn,k is (k−2)-SMVC, (n−3)-SMEC of order 1, (2n−8)-SMEC of order 2 and (3n−15)-SMEC of order 3. Moreover, we give the conditions when the four bounds are sharp respectively.

Suggested Citation

  • Guo, Jia, 2023. "On strong Menger connectivity of (n,k)-bubble-sort networks," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004010
    DOI: 10.1016/j.amc.2023.128232
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    References listed on IDEAS

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    1. Guo, Jia & Lu, Mei & Wang, Xin, 2022. "The (strong) structure connectivity and (strong) substructure connectivity of the (n,k)-bubble-sort network," Applied Mathematics and Computation, Elsevier, vol. 425(C).
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