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Bicyclic oriented graphs with skew-rank 6

Author

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  • Lu, Yong
  • Wang, Ligong
  • Zhou, Qiannan

Abstract

Let Gσ be an oriented graph and S(Gσ) be its skew-adjacency matrix. The skew-rank of Gσ, denoted by sr(Gσ), is the rank of S(Gσ). In this paper, we characterize all the bicyclic oriented graphs with skew-rank 6. Let Gσ be a bicyclic oriented graph with pendant vertices but no pendant twins. If sr(Gσ)=6, then 6 ≤ |V(Gσ)| ≤ 10.

Suggested Citation

  • Lu, Yong & Wang, Ligong & Zhou, Qiannan, 2015. "Bicyclic oriented graphs with skew-rank 6," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 899-908.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:899-908
    DOI: 10.1016/j.amc.2015.08.105
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    References listed on IDEAS

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    1. Qu, Hui & Yu, Guihai, 2015. "Bicyclic oriented graphs with skew-rank 2 or 4," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 182-191.
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    Cited by:

    1. Jinling Yang & Ligong Wang & Xiuwen Yang, 2021. "Some mixed graphs with H-rank 4, 6 or 8," Journal of Combinatorial Optimization, Springer, vol. 41(3), pages 678-693, April.
    2. Jing Huang & Shuchao Li & Hua Wang, 2018. "Relation between the skew-rank of an oriented graph and the independence number of its underlying graph," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 65-80, July.
    3. Yong Lu & Ligong Wang & Qiannan Zhou, 2019. "The rank of a complex unit gain graph in terms of the rank of its underlying graph," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 570-588, August.

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    4. Jing Huang & Shuchao Li & Hua Wang, 2018. "Relation between the skew-rank of an oriented graph and the independence number of its underlying graph," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 65-80, July.

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