INDUCED REGULAR PERFECT GRAPHS

Title

INDUCED REGULAR PERFECT GRAPHS

Creator

Jayakumar G.S.; Sangeetha V.

Description

A graph G is said to be R-perfect if, for all induced subgraphs H of G, the induced regular independence number of each induced subgraph H is equal to its corresponding induced regular cover. Here, the induced regular independence number is the maximum number of vertices in H such that no two belong to the same induced regular subgraph in H, and the induced regular cover of H is the minimum number of induced regular subgraphs in H required to cover the vertex set of H. This article introduces the notion of induced regular perfect graphs or R-perfect graphs through which we study the structural properties of R-perfect graphs and identify a forbidden class of graphs for the same. This further leads to the characterization of R-perfect biconnected graphs. With these results, we derive and prove a general characterization for R-perfect graphs. 2023, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved.

Source

South East Asian Journal of Mathematics and Mathematical Sciences, Vol-19, No. 3, pp. 285-300.

Date

2023-01-01

Publisher

RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES

Subject

F-perfect graphs; Graph minors; Perfect graphs; R-perfect graphs; Regular graphs

Coverage

Jayakumar G.S., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India; Sangeetha V., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India

Rights

Restricted Access

Relation

ISSN: 9727752

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.56827/SEAJMMS.2023.1903.23

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