An Interplay between Commutative Rings and Graph Theory: A Review | Chapter 10 | Advancements in Science and Technology: Paving the Way to a Sustainable Future

The study of zero-divisor graphs has emerged as a key area of research in algebra, serving as a link between ring theory and graph theory. These graphs offer a valuable framework for exploring the structure of commutative rings. While many important findings have previously been established in the study of graphs associated with zero-divisors of a commutative ring, this chapter highlights some of the key findings that directly demonstrate the connection between algebra and graph theory.

 

Author (s) Details

Hem Lata
G.G.D.S.D. College, Hariana, Hoshiarpur, India.

 

Shelly Garg
DAV University, Jalandhar, India.

 

Please see the book here:-  https://doi.org/10.9734/bpi/mono/978-93-49473-39-3/CH10

Assessment of Distance Related Spectrum of the Zero-divisor Graph | Chapter 05 | Novel Research Aspects in Mathematical and Computer Science Vol. 2

 For various values of n, the goal of this work is to discover the distance, distance Laplacian, and distance signless Laplacian of Denote the set of nonzero zero-divisors of R for a commutative ring with non-zero identity. The R zero-divisor graph (R) is a simple undirected graph with all non-zero zero-divisors as vertices and two different vertices adjacent only if and only if xy = 0. The distance, distance Laplacian, and distance singless Laplacian spectrum for n = p3 and pq are examined in this study. Our decision to employ matrices in the spectrum computation was influenced by the distinctive combinatorial structure as well as the usual block structure of the distance related matrices of the graphs discussed in this paper.

Author(S) Details

P. M. Magi
Department of Mathematics, Panampilly Memorial Govt. College, Chalakudy, Kerala, India.

View Book:- https://stm.bookpi.org/NRAMCS-V2/article/view/6791