ODD SUN-FREE TRIANGULATED GRAPHS ARE S-PERFECT

Title

ODD SUN-FREE TRIANGULATED GRAPHS ARE S-PERFECT

Creator

Ravindra, G.; Ghosh, Sanghita; Abraham, V.M.

Description

For a graph G with the vertex set V (G) and the edge set E(G) and a star subgraph S of G, let ?S(G) be the maximum number of vertices in G such that no two of them are in the same star subgraph S and ?S(G) be the minimum number of star sub-graph S that cover the vertices of G. A graph G is called S-perfect if for every induced subgraph H of G, ?S(H) = ?S(H). Motivated by perfect graphs discovered by Berge, Ravindra in-troduced S-perfect graphs. In this paper we prove that a trian-gulated graph is S-perfect if and only if G is odd sun-free. This result leads to a conjecture which if proved is a structural char-acterization of S-perfect graphs in terms of forbidden subgraphs. 2025, Diogenes Co. Ltd.. All rights reserved.

Source

International Journal of Applied Mathematics;Volume;38;Issue;2S;pp.423-432

Date

01-01-2025

Publisher

Diogenes Co. Ltd.

Subject

Extended sun graph; S-perfect graphs; Sun graph

Coverage

Ravindra G., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Ghosh S., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Abraham V.M., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 13111728;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.12732/ijam.v38i2s.92

https://www.scopus.com/pages/publications/105017183803?origin=resultslist