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The bipartite unicyclic graphs with the first ⌊n−34⌋ largest matching energies

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  • Chen, Lin
  • Liu, Jinfeng

Abstract

The theory of matching energy of graphs since been proposed by Gutman and Wagner in 2012, has attracted more and more attention. It is denoted by Bn,m, the class of bipartite graphs with order n and size m. In particular, Bn,n denotes the set of bipartite unicyclic graphs, which is an interesting class of graphs. In this paper, for odd n, we characterize the bipartite unicyclic graphs with the first ⌊n−34⌋ largest matching energies. There is an interesting correspondence: we conclude that the graph with the second maximal matching energy in Bn,n for odd n ≥ 11 is Pn6, which is the only graph attaining the maximum value of the energy among all the (bipartite) unicyclic graphs for n ≥ 16.

Suggested Citation

  • Chen, Lin & Liu, Jinfeng, 2015. "The bipartite unicyclic graphs with the first ⌊n−34⌋ largest matching energies," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 644-656.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:644-656
    DOI: 10.1016/j.amc.2015.06.115
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    Cited by:

    1. Li, Hong-Hai & Wu, Qian-Qian & Gutman, Ivan, 2016. "On ordering of complements of graphs with respect to matching numbers," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 167-174.
    2. Chen, Lin & Liu, Jinfeng, 2016. "Extremal values of matching energies of one class of graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 976-992.
    3. Xiaolin Chen & Huishu Lian, 2019. "Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs," Complexity, Hindawi, vol. 2019, pages 1-7, April.

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