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Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs

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  • Xiaolin Chen
  • Huishu Lian

Abstract

The matching energy of a graph was introduced by Gutman and Wagner, which is defined as the sum of the absolute values of the roots of the matching polynomial . The largest matching root is the largest root of the matching polynomial . Let denote the complete - partite graph with order , where . In this paper, we prove that, for the given values and , both the matching energy and the largest matching root of complete - partite graphs are minimal for complete split graph and are maximal for Turán graph .

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:9728976
    DOI: 10.1155/2019/9728976
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    References listed on IDEAS

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    1. 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.
    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. Monsalve, Juan & Rada, Juan & Shi, Yongtang, 2019. "Extremal values of energy over oriented bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 26-34.
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