Proof of a conjecture on Sombor index

Habibi, Mohammad; Singh, Randhir

doi:10.22061/jdma.2025.11904.1126

Proof of a conjecture on Sombor index

Document Type : Short Communication

Authors

Mohammad Habibi ¹
Randhir Singh ²

¹ Department of Mathematics, Tafresh University, Tafresh 39518-79611, I. R. Iran

² Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India.

10.22061/jdma.2025.11904.1126

Abstract

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.93 (2025) 853-859] 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.

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Main Subjects