Extremal iota energy of bicyclic digraphs

Rashid Farooq, Mehtab Khan and Faiz Ahmad

Applied Mathematics and Computation, 2017, vol. 303, issue C, 24-33

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.

Keywords: Energy of digraphs; Iota energy of digraphs; Bicyclic digraphs (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:303:y:2017:i:c:p:24-33

DOI: 10.1016/j.amc.2017.01.028

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