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

被引：14

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 20 条

[1] The zero-divisor graph of a commutative ring [J].