Further studies on chromatic completion of graphs

Title

Further studies on chromatic completion of graphs

Creator

Antony, Toby B.; Naduvath, Sudev

Description

The chromatic completion graph of G with respect to a proper vertex coloring c of G, denoted by Gc?, is the graph obtained by adding all possible edges to G without violating the proper coloring protocol. The maximum number of edges added to G to obtain the chromatic completion graph is the chromatic completion number ??(G). Equitable chromatic completion graph Ge? of a graph G and equitable chromatic completion number ??e(G) are the equitable analogues of Gc? and ??(G), respectively. In this paper, we present various structural aspects of chromatic completion graphs and equitable chromatic completion graphs. Also, the chromatic completion and the related parameter are described in terms of adjacency matrix and color matrix of graphs. The equitable chromatic completion graph is shown to be a Tur graph. More relevantly, we obtained the equitable chromatic completion number of an arbitrary graph G. World Scientific Publishing Company.

Source

Discrete Mathematics, Algorithms and Applications;Volume;18;Issue;2;Article No.;2550032;

Date

01-01-2026

Publisher

World Scientific

Subject

chromatic completion graph; chromatic completion number; equitable chromatic completion graph; equitable chromatic completion number; Proper edge

Coverage

Antony T.B., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 17938309;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793830925500326

https://www.scopus.com/pages/publications/105008671341?origin=resultslist