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Relationship between the rank and the matching number of a graph

Author

Listed:
  • Feng, Zhimin
  • Huang, Jing
  • Li, Shuchao
  • Luo, Xiaobing

Abstract

Given a simple graph G, let A(G) be its adjacency matrix and α′(G) be its matching number. The rank of G, written as r(G), refers to the rank of A(G). In this paper, some relations between the rank and the matching number of a graph are studied. Firstly, it is proved that −2d(G)⩽r(G)−2α′(G)⩽No, where d(G) and No are, respectively, the dimension of cycle space and the number of odd cycles of G. Secondly, sharp lower bounds on both r(G)−α′(G) and r(G)/α′(G) are determined. All the corresponding extremal graphs are characterized, respectively.

Suggested Citation

  • Feng, Zhimin & Huang, Jing & Li, Shuchao & Luo, Xiaobing, 2019. "Relationship between the rank and the matching number of a graph," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 411-421.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:411-421
    DOI: 10.1016/j.amc.2019.02.055
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    References listed on IDEAS

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    1. 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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    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.

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    More about this item

    Keywords

    Rank; Nullity; Matching number;
    All these keywords.

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