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

Jia Guo

Applied Mathematics and Computation, 2023, vol. 458, issue C

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.

Keywords: Network; Strong Menger connectivity; (n, k)-Bubble-sort network (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004010

DOI: 10.1016/j.amc.2023.128232

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