Embedding spanning disjoint cycles in enhanced hypercube networks with prescribed vertices in each cycle

Qiao, Hongwei; Meng, Jixiang; Sabir, Eminjan

doi:10.1016/j.amc.2022.127481

Cited by 6 publications

(1 citation statement)

References 19 publications

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“…Consequently, embedding hamiltonian cycles (paths) into a network topology is crucial for the network simulation [9]. Thus, hamiltonicity and many variations on it have been widely studied, such as k-ordered hamiltonicity [10], hamiltonian decomposition [11], pancyclicity [12], spanning connectivity [13], and 2-factors (a 2-factor of a graph G is a spanning 2-regular subgraph of G) [14].…”

Section: Introductionmentioning

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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