On spectrum of Sombor matrix and Sombor energy of graphs

Shariefuddin Pirzada*, Bilal Ahmad Rather, Kinkar Chandra Das, Yilun Shang, Ivan Gutman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Sombor index ( SO ) is a recently introduced degree-based graph invariant, defined as the sum over all pairs of adjacent vertices u,v of the term √d2u+d2v , where du and dv denote the degrees of vertices u and v, respectively. The matrix associated with SO is the Sombor matrix, and its spectrum is the Sombor spectrum. In this paper, the connected graphs having exactly two and exactly three Sombor eigenvalues are characterized. Bounds are obtained for the spectral radius and energy of the Sombor matrix, and the corresponding extremal graphs are determined. In addition, the Sombor spectra of several families of graphs are calculated.
Original languageEnglish
JournalGeorgian Mathematical Journal
Early online date13 Jan 2025
DOIs
Publication statusE-pub ahead of print - 13 Jan 2025

Keywords

  • Sombor index
  • Sombor matrix
  • Sombor spectrum
  • Sombor spectral radius
  • Sombor energy

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