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Two-disjoint-cycle-cover vertex bipancyclicity of the bipartite generalized hypercube

Author

Listed:
  • Niu, Ruichao
  • Xu, Min
  • Lai, Hong-Jian

Abstract

Let r2≥r1≥0 be two integers. A bipartite graph G is two-disjoint-cycle-cover vertex [r1,r2]-bipancyclic (2-DCC vertex [r1,r2]-bipancyclic in short) if for any two vertices u,v∈V(G) and any even integer ℓ satisfying r1≤ℓ≤r2, there exist two vertex-disjoint cycles J1 and J2 in G with |V(J1)|=ℓ and |V(J2)|=|V(G)|−ℓ such that u∈V(J1) and v∈V(J2); and there also exist two vertex-disjoint cycles J1′ and J2′ in G with |V(J1′)|=ℓ and |V(J2′)|=|V(G)|−ℓ such that v∈V(J1′) and u∈V(J2′). We study the 2-DCC vertex bipancyclicity of the n-dimensional bipartite generalized hypercube C(d1,d2,…,dn). As a result, we determine a family of exceptional graphs and show that for all integers n≥2, an n-dimensional bipartite generalized hypercube G is 2-DCC vertex [4,|V(G)|/2]-bipancyclic if and only if G is not a member in this family. Furthermore, as applications, we prove the vertex-bipancyclicity and 2-DCC bipancyclicity on n-dimensional bipartite generalized hypercube and show that the similar properties also hold for all n-dimensional bipartite k-ary n-cubes, for n≥2.

Suggested Citation

  • Niu, Ruichao & Xu, Min & Lai, Hong-Jian, 2021. "Two-disjoint-cycle-cover vertex bipancyclicity of the bipartite generalized hypercube," Applied Mathematics and Computation, Elsevier, vol. 400(C).
  • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321001387
    DOI: 10.1016/j.amc.2021.126090
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    Cited by:

    1. Hao, Rong-Xia & Qin, Xiao-Wen & Zhang, Hui & Chang, Jou-Ming, 2024. "Two-disjoint-cycle-cover pancyclicity of data center networks," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    2. Cheng, Dongqin, 2022. "Two disjoint cycles of various lengths in alternating group graph," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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