Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube

Da-Wei Yang, Zihao Xu, Yan-Quan Feng and Jaeun Lee

Applied Mathematics and Computation, 2023, vol. 452, issue C

Abstract: The spined cube SQn, as a variant network of the hypercube Qn, was proposed in 2011 and has attracted much attention because of its smaller diameter. It is well-known that Qn is a Cayley graph. In the present paper, we show that SQn is an m-Cayley graph, that is its automorphism group has a semiregular subgroup acting on the vertices with m orbits, where m=4 when n≥6 and m=⌊n/2⌋ when n≤5. Consequently, it shows that an SQn with n≥6 can be partitioned into eight disjoint hypercubes of dimension n−3. As an application, it is proved that there exist two edge-disjoint Hamiltonian cycles in SQn when n≥4. Moreover, we prove that SQn is not vertex-transitive unless n≤3.

Keywords: Interconnection network; The spined cube; 4-Cayley graphs; Hamiltonian cycles (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:452:y:2023:i:c:s0096300323002448

DOI: 10.1016/j.amc.2023.128075

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