2-spanning cyclability problems of the some generalized Petersen graphs

Yang, Meng-Chien; Hsu, Lih‐Hsing; Hung, Chun-Nan; Cheng, Eddie

doi:10.7151/dmgt.2150

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…Shinde and Borse proved that the n-dimensional tori is spanning k-cyclable for 1 ≤ k ≤ 2n − 1 [23]. Yang and Hsu proved that the generalized Petersen graph GP(n, k) is spanning 2-cyclable for k ≤ 4 [24]. Recently, Qiao et al proved that the enhanced hypercube [25].…”

Section: Conjecture 2 ([17]mentioning

confidence: 99%

Embedding Spanning Disjoint Cycles in Hypercube Networks with Prescribed Edges in Each Cycle

Wu,

Sabir

2023

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One of the important issues in evaluating an interconnection network is to study the hamiltonian cycle embedding problems. A graph G is spanning k-edge-cyclable if for any k independent edges e1,e2,…,ek of G, there exist k vertex-disjoint cycles C1,C2,…,Ck in G such that V(C1)∪V(C2)∪⋯∪V(Ck)=V(G) and ei∈E(Ci) for all 1≤i≤k. According to the definition, the problem of finding hamiltonian cycle focuses on k=1. The notion of spanning edge-cyclability can be applied to the problem of identifying faulty links and other related issues in interconnection networks. In this paper, we prove that the n-dimensional hypercube Qn is spanning k-edge-cyclable for 1≤k≤n−1 and n≥2. This is the best possible result, in the sense that the n-dimensional hypercube Qn is not spanning n-edge-cyclable.

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Section: Conjecture 2 ([17]mentioning

confidence: 99%