A survey on the intersection graphs of ideals of rings

Title

A survey on the intersection graphs of ideals of rings

Creator

Chakrabarty I.; Kureethara J.V.

Description

Let L(R) denote the set of all non-trivial left ideals of a ring R. The intersection graph of ideals of a ring R is an undirected simple graph denoted by G(R) whose vertices are in a one-to-one correspondence with L(R) and two distinct vertices are joined by an edge if and only if the corresponding left ideals of R have a non-zero intersection. The ideal structure of a ring reects many ring theoretical properties. There is so much research that has been conducted during the last decade to explore the properties of G(R). This is a survey of the developments in the study on the intersection graphs of ideals of rings since its introduction in 2009. 2022 by the authors.

Source

Communications in Combinatorics and Optimization, Vol-7, No. 2, pp. 121-167.

Date

2022-01-01

Publisher

Azarbaijan Shahid Madani University

Subject

chromatic number; genus; ideal of a ring; intersection graph; Ring

Coverage

Chakrabarty I., Department of Mathematics, CHRIST (Deemed to be University), Hosur Road, Bengaluru, 560029, India; Kureethara J.V., Department of Mathematics, CHRIST (Deemed to be University), Hosur Road, Bengaluru, 560029, India

Rights

Restricted Access

Relation

ISSN: 25382128

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.22049/CCO.2021.26990.1176

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