Lower Bounds on the Entire Sombor Index

Document Type : Research Paper


Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran


‎Let $G=(V,E)$ be a graph‎. ‎The entire Sombor index of graph ‎$‎G‎$‎, $ SO^\varepsilon(G) $ is defined as the sum of the terms‎
‎$\sqrt{d_{G}^2(a)+d_{G}^2(b)}$‎, ‎where $a$ is either adjacent to or incident with $b$ and‎
‎$a,b\in V\cup E$‎.
‎It is known that if $T$ is a tree of order $n$‎, ‎then $SO^\varepsilon(T)\ge 6\sqrt{5}+8(n-3)\sqrt{2}$‎. ‎We improve this result and establish best lower bounds on the entire Sombor index with given vertices number and maximum degree‎. ‎Also‎, ‎we determine the extremal trees achieve these bounds.


Main Subjects

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