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Extremal Laplacian energy of directed trees, unicyclic digraphs and bicyclic digraphs

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  • Yang, Xiuwen
  • Wang, Ligong

Abstract

Let A(G) and D+(G) be the adjacency matrix of a digraph G with n vertices and the diagonal matrix of vertex outdegrees of G, respectively. Then the Laplacian matrix of the digraph G is L(G)=D+(G)−A(G). The Laplacian energy of a digraph G is defined as LE(G)=∑i=1nλi2 by using second spectral moment, where λ1,λ2,…,λn are all the eigenvalues of L(G) of G. In this paper, by using arc shifting operation and out-star shifting operation, we determine the directed trees, unicyclic digraphs and bicyclic digraphs which attain maximal and minimal Laplacian energy among all digraphs with n vertices, respectively.

Suggested Citation

  • Yang, Xiuwen & Wang, Ligong, 2020. "Extremal Laplacian energy of directed trees, unicyclic digraphs and bicyclic digraphs," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307295
    DOI: 10.1016/j.amc.2019.124737
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    References listed on IDEAS

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    1. Wang, Wen-Huan, 2016. "Ordering of oriented unicyclic graphs by skew energies," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 136-148.
    2. Monsalve, Juan & Rada, Juan, 2016. "Bicyclic digraphs with maximal energy," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 124-131.
    3. Yang, Xiuwen & Wang, Ligong, 2018. "On the ordering of bicyclic digraphs with respect to energy and iota energy," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 768-778.
    4. Guo, Lifeng & Wang, Ligong & Xiao, Peng, 2017. "5-regular oriented graphs with optimum skew energy," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 43-59.
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