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

Author

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

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.

Suggested Citation

  • Yang, Da-Wei & Xu, Zihao & Feng, Yan-Quan & Lee, Jaeun, 2023. "Symmetric property and edge-disjoint Hamiltonian cycles of the spined cube," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    • Handle: RePEc:eee:apmaco:v:452:y:2023:i:c:s0096300323002448
    DOI: 10.1016/j.amc.2023.128075
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    Cited by:

    1. Kung-Jui Pai, 2023. "Three Edge-Disjoint Hamiltonian Cycles in Folded Locally Twisted Cubes and Folded Crossed Cubes with Applications to All-to-All Broadcasting," Mathematics, MDPI, vol. 11(15), pages 1-14, August.

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