EXTREMAL VALUES ON THE MODIFIED SOMBOR INDEX OF TREES AND UNICYCLIC GRAPHS

Raghavendra H Kashyap     (School of Arts Sciences Humanities & Education, SASTRA Deemed University, Thanjavur, India)
Yanamandram B Venkatakrishnan     (School of Arts Sciences Humanities & Education, SASTRA Deemed University, Thanjavur, India)
Rashad Ismail     (Department of Mathematics, Faculty of Science and Arts, King Khalid University, Mahayl Assir 61913, Saudi Arabia)
Selvaraj Balachandran     (School of Arts Sciences Humanities & Education, SASTRA Deemed University, Thanjavur, India)
Hari Naresh Kumar     (School of Arts Sciences Humanities & Education, SASTRA Deemed University, Thanjavur, India)

Abstract


Let \(G=(V,E)\) be a simple connected graph. The modified Sombor index denoted by \(mSo(G)\) is defined as $$mSo(G)=\sum_{uv\in E}\frac{1}{\sqrt{d^2_u+d^2_v}},$$ where \(d_v\) denotes the degree of vertex \(v\). In this paper we present extremal values of modified Sombor index  over the set of trees and unicyclic graphs.

Keywords


Modified Sombor Index, Trees, Unicyclic graphs, Extremal values

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References


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DOI: http://dx.doi.org/10.15826/umj.2024.1.006

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