TY - JOUR

T1 - Sharp Bounds on the Sombor Energy of Graphs

AU - Rather, Bilal Ahmad

AU - Imran, Muhammad

N1 - Funding Information:
Acknowledgment: The authors are very thankful to the reviewers for their valuable comments that improved the manuscript. This research is supported by Asian Universities Alliance (AUA) grant of United Arab Emirates University via Grant No. G00003461.
Publisher Copyright:
© 2022 University of Kragujevac, Faculty of Science. All rights reserved.

PY - 2022

Y1 - 2022

N2 - For a simple graph G with vertex set {v1, v2, . . ., vn} and edge set E(G). The Sombor matrix S(G) of G is an n × n matrix, whose (i, j)-entry is equal is q d2i + d2j, if i and j are adjacent and 0, otherwise. The multi-set of the eigenvalues of S(G) is known as the Sombor spectrum of G, denoted by µ1 ≥ µ2 ≥ · · · ≥ µn, where µ1 is the Sombor spectral radius of G. The absolute sum of the Sombor eigenvalues if known as the Sombor energy. In this article, we find the bounds for the Sombor energy of G and characterize the corresponding extremal graphs. These bounds are better than already known results on Sombor energy.

AB - For a simple graph G with vertex set {v1, v2, . . ., vn} and edge set E(G). The Sombor matrix S(G) of G is an n × n matrix, whose (i, j)-entry is equal is q d2i + d2j, if i and j are adjacent and 0, otherwise. The multi-set of the eigenvalues of S(G) is known as the Sombor spectrum of G, denoted by µ1 ≥ µ2 ≥ · · · ≥ µn, where µ1 is the Sombor spectral radius of G. The absolute sum of the Sombor eigenvalues if known as the Sombor energy. In this article, we find the bounds for the Sombor energy of G and characterize the corresponding extremal graphs. These bounds are better than already known results on Sombor energy.

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U2 - 10.46793/match.88-3.605R

DO - 10.46793/match.88-3.605R

M3 - Article

AN - SCOPUS:85129525324

SN - 0340-6253

VL - 88

SP - 605

EP - 624

JO - Match

JF - Match

IS - 3

ER -