Open AccessOn the inverse sum indeg index (\(ISI\)), spectral radius of \(ISI\) matrix and \(ISI\) energy
Author(s) -
Özge Çolakoğlu Havare
Publication year - 2022
Publication title -
open journal of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 2616-4906
pISSN - 2523-0212
DOI - 10.30538/oms2022.0176
Subject(s) - inverse , mathematics , spectral radius , combinatorics , matrix (chemical analysis) , radius , energy (signal processing) , mathematical analysis , physics , quantum mechanics , eigenvalues and eigenvectors , statistics , geometry , chemistry , computer science , computer security , chromatography
The inverse sum indeg index \(ISI(G)\) of a graph is equal to the sum over all edges \(uv\in E(G)\) of weights \(\frac{d_{u}d_{v}}{d_{u}+d_{v}}\). This paper presents the relation between the inverse sum indeg index and the chromatic number. The bounds for the spectral radius of the inverse sum indeg matrix and the inverse sum indeg energy are obtained. Additionally, the Nordhaus-Gaddum-type results for the inverse sum indeg index, the inverse sum indeg energy and the spectral radius of the inverse sum index matrix are given.