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Extremal iota energy of bicyclic digraphs

Author

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  • Farooq, Rashid
  • Khan, Mehtab
  • Ahmad, Faiz

Abstract

The energy of an n-vertex digraph D is defined by E(D)=∑k=1n|Re(zk)|, where z1,…,zn are eigenvalues of D and Re(zk) is the real part of eigenvalue zk. Very recently, a new type of energy of digraphs has been introduced, which is known as the iota energy of digraphs. The iota energy of the digraph D is defined by Ec(D)=∑k=1n|Im(zk)|, where z1,…,zn are eigenvalues of D and Im(zk) is the imaginary part of eigenvalue zk. The unicyclic digraphs with extremal iota energy are known. In this paper, we consider a class Dn of n-vertex bicyclic digraphs with vertex-disjoint directed cycles and find the digraphs in Dn with minimal and maximal iota energy.

Suggested Citation

  • Farooq, Rashid & Khan, Mehtab & Ahmad, Faiz, 2017. "Extremal iota energy of bicyclic digraphs," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 24-33.
    • Handle: RePEc:eee:apmaco:v:303:y:2017:i:c:p:24-33
    DOI: 10.1016/j.amc.2017.01.028
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    References listed on IDEAS

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    1. Monsalve, Juan & Rada, Juan, 2016. "Bicyclic digraphs with maximal energy," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 124-131.
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    Cited by:

    1. 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.

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