Packing internally disjoint Steiner trees to compute the κ3-connectivity in augmented cubes

Wei, Chao; Hao, Rong‐Xia; Chang, Jou–Ming

doi:10.1016/j.jpdc.2021.04.004

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2022

2024

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Cited by 10 publications

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“…To decide whether there exist k internally edge disjoint S-Steiner trees is NP-complete for a graph [6]. The generalized 3connectivities of augmented cubes, (n, k)-bubble-sort graphs, and generalized hypercubes have been obtained in [7][8][9], respectively. The generalized 4-connectivities of hypercubes, crossed cubes, exchanged hypercubes, and hierarchical cubic networks have been obtained in [10][11][12][13], respectively.…”

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confidence: 99%

The Generalized 3-Connectivity of Exchanged Folded Hypercubes

Ning,

2024

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For S⊆V(G),κG(S) denotes the maximum number k of edge disjoint trees T1,T2,…,Tk in G, such that V(Ti)∩V(Tj)=S for any i,j∈{1,2,…,k} and i≠j. For an integer 2≤r≤|V(G)|, the generalized r-connectivity of G is defined as κr(G)=min{κG(S)|S⊆V(G)and|S|=r}. In fact, κ2(G) is the traditional connectivity of G. Hence, the generalized r-connectivity is an extension of traditional connectivity. The exchanged folded hypercube EFH(s,t), in which s≥1 and t≥1 are positive integers, is a variant of the hypercube. In this paper, we find that κ3(EFH(s,t))=s+1 with 3≤s≤t.

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