Sombor index and eigenvalues of comaximal graphs of commutative rings

Bilal Ahmad Rather; Muhammed Imran; S. Pirzada

doi:10.1142/S0219498824501159

Sombor index and eigenvalues of comaximal graphs of commutative rings

Bilal Ahmad Rather, Muhammed Imran, S. Pirzada

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The comaximal graph Σ(R) of a commutative ring R is a simple graph with vertex set R and two distinct vertices u and v of Σ(R) are adjacent if and only if uR + vR = R. In this paper, we find the sharp bounds for the Sombor index for comaximal graphs of integer modulo ring ℤn and give the corresponding extremal graphs. Also, we find the Sombor eigenvalues and the bounds for the Sombor energy of comaximal graphs of ℤn.

Original language	English
Article number	2450115
Journal	Journal of Algebra and its Applications
DOIs	https://doi.org/10.1142/S0219498824501159
Publication status	Accepted/In press - 2023

Keywords

Adjacency matrix
eigenvalues, integers
Sombor index
Sombor matrix, comaximal graphs

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

Access to Document

10.1142/S0219498824501159

Cite this

@article{f4fdbfcd4037458d999b1e48c4846a84,

title = "Sombor index and eigenvalues of comaximal graphs of commutative rings",

abstract = "The comaximal graph Σ(R) of a commutative ring R is a simple graph with vertex set R and two distinct vertices u and v of Σ(R) are adjacent if and only if uR + vR = R. In this paper, we find the sharp bounds for the Sombor index for comaximal graphs of integer modulo ring ℤn and give the corresponding extremal graphs. Also, we find the Sombor eigenvalues and the bounds for the Sombor energy of comaximal graphs of ℤn.",

keywords = "Adjacency matrix, eigenvalues, integers, Sombor index, Sombor matrix, comaximal graphs",

author = "Rather, {Bilal Ahmad} and Muhammed Imran and S. Pirzada",

note = "Publisher Copyright: {\textcopyright} 2024 World Scientific Publishing Company.",

year = "2023",

doi = "10.1142/S0219498824501159",

language = "English",

journal = "Journal of Algebra and its Applications",

issn = "0219-4988",

publisher = "World Scientific Publishing Co. Pte Ltd",

}

TY - JOUR

T1 - Sombor index and eigenvalues of comaximal graphs of commutative rings

AU - Rather, Bilal Ahmad

AU - Imran, Muhammed

AU - Pirzada, S.

PY - 2023

Y1 - 2023

N2 - The comaximal graph Σ(R) of a commutative ring R is a simple graph with vertex set R and two distinct vertices u and v of Σ(R) are adjacent if and only if uR + vR = R. In this paper, we find the sharp bounds for the Sombor index for comaximal graphs of integer modulo ring ℤn and give the corresponding extremal graphs. Also, we find the Sombor eigenvalues and the bounds for the Sombor energy of comaximal graphs of ℤn.

AB - The comaximal graph Σ(R) of a commutative ring R is a simple graph with vertex set R and two distinct vertices u and v of Σ(R) are adjacent if and only if uR + vR = R. In this paper, we find the sharp bounds for the Sombor index for comaximal graphs of integer modulo ring ℤn and give the corresponding extremal graphs. Also, we find the Sombor eigenvalues and the bounds for the Sombor energy of comaximal graphs of ℤn.

KW - Adjacency matrix

KW - eigenvalues, integers

KW - Sombor index

KW - Sombor matrix, comaximal graphs

UR - http://www.scopus.com/inward/record.url?scp=85145942434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85145942434&partnerID=8YFLogxK

U2 - 10.1142/S0219498824501159

DO - 10.1142/S0219498824501159

M3 - Article

AN - SCOPUS:85145942434

SN - 0219-4988

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

M1 - 2450115

ER -

Sombor index and eigenvalues of comaximal graphs of commutative rings

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this