Bounds of modified Sombor index, spectral radius and energy

Let $ G $ be a simple graph with edge set $ E(G) $. The modified Sombor index is defined as $ ^{m}SO(G) = \sum\limits_{uv\in E(G)}\frac{1}{\sqrt{d_{u}^{2}~~+~~d_{v}^{2}}} $, where $ d_{u} $ (resp. $ d_{v} $) denotes the degree of vertex $ u $ (resp. $ v $). In this paper, we determine some bounds fo...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 10; pp. 11263 - 11274
Main Authors Huang, Yufei, Liu, Hechao
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
extremal value
modified sombor index
modified sombor spectral radius
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Summary:Let $ G $ be a simple graph with edge set $ E(G) $. The modified Sombor index is defined as $ ^{m}SO(G) = \sum\limits_{uv\in E(G)}\frac{1}{\sqrt{d_{u}^{2}~~+~~d_{v}^{2}}} $, where $ d_{u} $ (resp. $ d_{v} $) denotes the degree of vertex $ u $ (resp. $ v $). In this paper, we determine some bounds for the modified Sombor indices of graphs with given some parameters (e.g., maximum degree $ \Delta $, minimum degree $ \delta $, diameter $ d $, girth $ g $) and the Nordhaus-Gaddum-type results. We also obtain the relationship between modified Sombor index and some other indices. At last, we obtain some bounds for the modified spectral radius and energy.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021653