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Ural Math. J., 2024 Volume 10, Issue 1, Pages 68–75 (Mi umj221)

Extremal values on the modified Sombor index of trees and unicyclic graphs

Raghavendra H. Kashyapa, Yanamandram B. Venkatakrishnana, Rashad Ismailb, Selvaraj Balachandrana, Hari Naresh Kumara

a SASTRA Deemed University, Thanjavur
b King Khalid University

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

Language: English

DOI: 10.15826/umj.2024.1.006



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