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On the ordering of bicyclic digraphs with respect to energy and iota energy

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  • Yang, Xiuwen
  • Wang, Ligong

Abstract

Let z1,z2,…,zn be eigenvalues of the adjacency matrix of an n-vertex digraph D. Let Re(zk) and Im(zk) denote the real part and the imaginary part of eigenvalue zk, respectively. The energy of an n-vertex digraph D is defined as E(D)=∑k=1n|Re(zk)|. Recently, the concept of energy of digraphs is extended to iota energy of digraphs. The iota energy of an n-vertex digraph D is defined as Ec(D)=∑k=1n|Im(zk)|. In this paper, we investigate the energy and iota energy about a class Dn of n-vertex bicyclic digraphs with vertex-disjoint two directed even cycles and characterize the digraphs in Dn with maximal and minimal energy or iota energy. Moreover, we determine the whole ordering in Dn with respect to energy and iota energy, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:768-778
    DOI: 10.1016/j.amc.2018.07.067
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    References listed on IDEAS

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    1. Farooq, Rashid & Khan, Mehtab & Ahmad, Faiz, 2017. "Extremal iota energy of bicyclic digraphs," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 24-33.
    2. Monsalve, Juan & Rada, Juan, 2016. "Bicyclic digraphs with maximal energy," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 124-131.
    3. 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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    Cited by:

    1. Yang, Xiuwen & Wang, Ligong, 2020. "Extremal Laplacian energy of directed trees, unicyclic digraphs and bicyclic digraphs," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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