Proof of a conjecture on Sombor index

Let G be a simple graph. In this paper we prove the stated conjecture in [Some notes on Sombor index of graphs, MATCH Commun. Math. Comput. Chem.۹۳ (۲۰۲۵) ۸۵۳-۸۵۹] and state an upper bound for the Sombor index of G in terms of its size and the smallest eigenvalue of its Sombor matrix. Also,characterize all graphs for which the specified bound is attained.

کلیدواژه ها:

Sombor index ، Sombor matrix ، eigenvalue