The 3-path-connectivity of the k-ary n-cube

Wen-Han Zhu, Rong-Xia Hao, Yan-Quan Feng and Jaeun Lee

Applied Mathematics and Computation, 2023, vol. 436, issue C

Abstract: Let G be a connected simple graph with vertex set V(G). Let Ω be a subset with cardinality at least two of V(G). A path containing all vertices of Ω is said to be an Ω-path of G. Two Ω-paths T1 and T2 of G are internally disjointif V(T1)∩V(T2)=Ω and E(T1)∩E(T2)=∅. For an integer ℓ with 2≤ℓ, the ℓ-path-connectivityπℓ(G) is defined as πℓ(G)=min{πG(Ω)|Ω⊆V(G) and |Ω|=ℓ}, where πG(Ω) represents the maximum number of internally disjoint Ω-paths. In this paper, we completely determine 3-path-connectivity of the k-ary n-cube Qnk. By deeply exploring the structural proprieties of Qnk, we show that π3(Qnk)=⌊6n−14⌋ with n≥1 and k≥3.

Keywords: K-ary n-cube; Regular graph; Path; Path-connectivity (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005732

DOI: 10.1016/j.amc.2022.127499

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