On normalized Laplacian spectrum of zero di-visor graphs of commutative ring Zn

被引：13

作者：

Pirzada, S. ^{[1
]}

Rather, Bilal A. ^{[1
]}

Chishti, T. A. ^{[1
]}

Samee, U. ^{[1
]}

机构：

[1] Univ Kashmir, Dept Math, Srinagar, Kashmir, India

来源：

ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS | 2021年 / 9卷 / 02期

关键词：

normalized Laplacian matrix; normalized Laplacian spectrum; zero divisor graph; DIVISOR GRAPH; EIGENVALUES;

D O I：

10.5614/ejgta.2021.9.2.7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a finite commutative ring Z(n) with identity 1 not equal 0, the zero divisor graph Gamma(Z(n)) is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices x and y are adjacent if and only if xy = 0. We find the normalized Laplacian spectrum of the zero divisor graphs Gamma (Z(n))for various values of n and characterize n for which Gamma (Z(n)) is normalized Laplacian integral. We also obtain bounds for the sum of graph invariant S-beta* (G)-the sum of the beta-th power of the non-zero normalized Laplacian eigenvalues of Gamma (Z(n)).

引用

页码：331 / 345

页数：15

共 43 条

[41] Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring ZpM1 qM2
Pirzada, S.
Rather, Bilal A.
ul Shaban, Rezwan
Chishti, T. A.
COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2022,
[42] Linear strand of edge ideals of zero divisor graphs of the ring Zn (vol 52, pg 5069, 2024)
Rather, Ahmad
Imran, Muhammed
Pirzad, S.
COMMUNICATIONS IN ALGEBRA, 2024,
[43] Exploring normalized distance Laplacian eigenvalues of the zero-divisor graph of ring Zn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_{n}$$\end{document}
Nadeem ur Rehman
Mohd Nazim
Rendiconti del Circolo Matematico di Palermo Series 2, 2024, 73 (2): : 515 - 526

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