On Some Topological Indices Defined via the Modified Sombor Matrix

Xuewu Zuo, Bilal Ahmad Rather, Muhammad Imran, Akbar Ali

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Let G be a simple graph with the vertex set (Formula presented.) and denote by (Formula presented.) the degree of the vertex (Formula presented.). The modified Sombor index of G is the addition of the numbers (Formula presented.) over all of the edges (Formula presented.) of G. The modified Sombor matrix (Formula presented.) of G is the n by n matrix such that its (Formula presented.) -entry is equal to (Formula presented.) when (Formula presented.) and (Formula presented.) are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of (Formula presented.). The sum of the absolute eigenvalues of (Formula presented.) is known as the modified Sombor energy of G. Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs. In this article, several bounds for the modified Sombor index, the modified Sombor spectral radius, and the modified Sombor energy are found, and the corresponding extremal graphs are characterized. By using computer programs (Mathematica and AutographiX), it is found that there exists only one pair of the modified Sombor equienergetic chemical graphs of an order of at most seven. It is proven that the modified Sombor energy of every regular, complete multipartite graph is (Formula presented.) ; this result gives a large class of the modified Sombor equienergetic graphs. The (linear, logarithmic, and quadratic) regression analyses of the modified Sombor index and the modified Sombor energy together with their classical versions are also performed for the boiling points of the chemical graphs of an order of at most seven.

Original languageEnglish
Article number6772
JournalMolecules
Volume27
Issue number19
DOIs
Publication statusPublished - Oct 2022

Keywords

  • Sombor index
  • adjacency matrix
  • correlation
  • modified Sombor energy
  • modified Sombor matrix

ASJC Scopus subject areas

  • Analytical Chemistry
  • Chemistry (miscellaneous)
  • Molecular Medicine
  • Pharmaceutical Science
  • Drug Discovery
  • Physical and Theoretical Chemistry
  • Organic Chemistry

Fingerprint

Dive into the research topics of 'On Some Topological Indices Defined via the Modified Sombor Matrix'. Together they form a unique fingerprint.

Cite this