The generalized 4-connectivity of exchanged hypercubes

Shu-Li Zhao and Rong-Xia Hao

Applied Mathematics and Computation, 2019, vol. 347, issue C, 342-353

Abstract: Let S ⊆ V(G) and κG(S) denote 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 r with 2 ≤ r ≤ n, the generalized r-connectivity of a graph G is defined as κr(G)=min{κG(S)|S⊆V(G) and |S|=r}. The parameter is a generalization of traditional connectivity. So far, almost all known results of κr(G) are about regular graphs and r=3. In this paper, we focus on κr(EH(s, t)) of the exchanged hypercube for r=4, where the exchanged hypercube EH(s, t) is not regular if s ≠ t. We show that κ4(EH(s,t))=min{s,t} for min{s, t} ≥ 3. As a corollary, we obtain that κ3(EH(s,t))=min{s,t} for min{s, t} ≥ 3.

Keywords: Generalized connectivity; Fault-tolerance; Reliability; Exchanged hypercube (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:342-353

DOI: 10.1016/j.amc.2018.11.023

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