Complex adjacency matrix and energy of digraphs. Issue 11 (2nd November 2017)

• Record Type: Journal Article
• Authors: Khan, Mehtab; Farooq, Rashid; Rada, Juan
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 11(2017)
• Page Start: 2170
• Page End: 2186
• Publication Date: 2017-11-02
• Subjects: Energy of digraphs -- complex adjacency matrix -- cyclic digraphs -- equienergetic digraphs; 05C35 -- 05C50; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2016.1265064
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. If D is a digraph of order n with eigenvalues, then its energy is defined by . We give a new notion of energy of digraphs defined by and call it the iota energy of the digraph D . It is shown that the Coulson's integral formula remains valid for iota energy. We also find the unicyclic digraphs with extremal iota energies among the class of unicyclic digraphs with a fixed order. Furthermore, it is shown that the iota energy is increasing over the set of n -vertex digraphs with cycles of length h, with respect to a quasi-order relation. We also generalize the increasing property of the energy over the set with respect to quasi-order relation.