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The Extendability of Cayley Graphs Generated by Transposition Trees

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  • Yongde Feng

    (School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou 730000, China
    College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China)

  • Yanting Xie

    (School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou 730000, China)

  • Fengxia Liu

    (College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China)

  • Shoujun Xu

    (School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou 730000, China)

Abstract

A connected graph Γ is k -extendable for a positive integer k if every matching M of size k can be extended to a perfect matching. The extendability number of Γ is the maximum k such that Γ is k -extendable. In this paper, we prove that Cayley graphs generated by transposition trees on { 1 , 2 , … , n } are ( n − 2 ) -extendable and determine that the extendability number is n − 2 for an integer n ≥ 3 .

Suggested Citation

  • Yongde Feng & Yanting Xie & Fengxia Liu & Shoujun Xu, 2022. "The Extendability of Cayley Graphs Generated by Transposition Trees," Mathematics, MDPI, vol. 10(9), pages 1-8, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1575-:d:810220
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    References listed on IDEAS

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    1. Jan Hackfeld & Arie M. C. A. Koster, 2018. "The matching extension problem in general graphs is co-NP-complete," Journal of Combinatorial Optimization, Springer, vol. 35(3), pages 853-859, April.
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    Cited by:

    1. Irina Cristea & Hashem Bordbar, 2023. "Preface to the Special Issue “Algebraic Structures and Graph Theory”," Mathematics, MDPI, vol. 11(15), pages 1-4, July.

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