Proof of a conjecture on Sombor index

Document Type : Short Communication

Authors

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

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

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.

Keywords

Main Subjects


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Volume 10, Issue 2
June 2025
Pages 157-160
  • Receive Date: 28 March 2025
  • Revise Date: 29 March 2025
  • Accept Date: 02 May 2025
  • First Publish Date: 01 June 2025
  • Publish Date: 01 June 2025