TY - JOUR
ID - 22707
TI - Iota energy of weighted digraphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Hafeez, Sumaira
AU - Khan, Mehtab
AD - School of Natural Sciences, National university of sciences and Technology Islamabad, Pakistan
AD - Department of mathematics, school of Natural Sciences, National University of Sciences and Technology Islamabad, Pakistan
Y1 - 2018
PY - 2018
VL - 7
IS - 3
SP - 55
EP - 73
KW - Weighted digraphs
KW - Extremal energy
KW - Equienergetic weighted digraphs
DO - 10.22108/toc.2018.109248.1546
N2 - The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. The iota energy of a digraph is recently defined as the sum of absolute values of imaginary part of its eigenvalues. In this paper, we extend the concept of iota energy of digraphs to weighted digraphs. We compute the iota energy formulae for the positive and negative weight directed cycles. We also characterize the unicyclic weighted digraphs with cycle weight $ r in [-1, 1]backslash {0}$ having minimum and maximum iota energy. We obtain well known McClelland upper bound for the iota energy of weighted digraphs. Finally, we find the class of noncospectral equienergetic weighted digraphs.
UR - http://toc.ui.ac.ir/article_22707.html
L1 - http://toc.ui.ac.ir/article_22707_8eb3ec61aa18a4a5a2445c45716a4a23.pdf
ER -