Iota energy of weighted digraphs
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 ene...
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University of Isfahan
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doaj-e9f65d35f9614ba7b2f425490111a2452020-11-24T22:08:03ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652018-09-0173557310.22108/toc.2018.109248.154622707Iota energy of weighted digraphsSumaira Hafeez0Mehtab Khan1School of Natural Sciences, National university of sciences and Technology Islamabad, PakistanDepartment of mathematics, school of Natural Sciences, National University of Sciences and Technology Islamabad, PakistanThe 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.http://toc.ui.ac.ir/article_22707_8eb3ec61aa18a4a5a2445c45716a4a23.pdfWeighted digraphsExtremal energyEquienergetic weighted digraphs |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sumaira Hafeez Mehtab Khan |
spellingShingle |
Sumaira Hafeez Mehtab Khan Iota energy of weighted digraphs Transactions on Combinatorics Weighted digraphs Extremal energy Equienergetic weighted digraphs |
author_facet |
Sumaira Hafeez Mehtab Khan |
author_sort |
Sumaira Hafeez |
title |
Iota energy of weighted digraphs |
title_short |
Iota energy of weighted digraphs |
title_full |
Iota energy of weighted digraphs |
title_fullStr |
Iota energy of weighted digraphs |
title_full_unstemmed |
Iota energy of weighted digraphs |
title_sort |
iota energy of weighted digraphs |
publisher |
University of Isfahan |
series |
Transactions on Combinatorics |
issn |
2251-8657 2251-8665 |
publishDate |
2018-09-01 |
description |
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. |
topic |
Weighted digraphs Extremal energy Equienergetic weighted digraphs |
url |
http://toc.ui.ac.ir/article_22707_8eb3ec61aa18a4a5a2445c45716a4a23.pdf |
work_keys_str_mv |
AT sumairahafeez iotaenergyofweighteddigraphs AT mehtabkhan iotaenergyofweighteddigraphs |
_version_ |
1725817875702218752 |