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 \(\varepsilon(G)\).
