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Title:
On Sombor Index and Graph Energy
Authors:
Mohammed Selim Reja, Shaikh Mohammed Abu Nayeem
doi:
Volume
89
Issue
2
Year
2023
Pages
451-466
Abstract Sombor index is a recently introduced degree based graph topological index. For a graph \(G\), it is defined as \[SO(G)=\sum_{uv\in E(G)}\sqrt{d_u^2+d_v^2},\] where \(d_u\) denotes the degree of the vertex \(u\) in \(G\). Within a short period of time after introduction of this index by Gutman, many aspects of it have been studied by many researchers. Relating the Sombor index \(SO(G)\) of a graph \(G\) with the energy \(\varepsilon(G)\) of \(G\) is one such instance among the others. In this article, we aim to provide some improved results relating \(SO(G)\) and \(\varepsilon(G)\).

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