Dominator and Total Dominator Colorings in Graphs

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

6 Citations (Scopus)

Abstract

A dominator coloring of a graph G is a proper coloring of the vertices of G in which each vertex of the graph dominates every vertex of some color class, where a vertex dominates itself and all vertices adjacent to it. The dominator chromatic number of G is the minimum number of colors among all dominator coloring of G. A total dominator coloring of a graph G is a proper coloring of the vertices of G in which each vertex of the graph dominates every vertex of some color class other than its own. The total dominator chromatic number of G is the minimum number of colors among all total dominator coloring of G. In this chapter, we present selected results on the dominator chromatic number and total dominator chromatic number of a graph.

Original languageEnglish
Title of host publicationDevelopments in Mathematics
PublisherSpringer
Pages101-133
Number of pages33
DOIs
Publication statusPublished - 2021

Publication series

NameDevelopments in Mathematics
Volume66
ISSN (Print)1389-2177
ISSN (Electronic)2197-795X

Keywords

  • Domination
  • Dominator coloring
  • Graph colorings
  • Total dominator coloring

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Dominator and Total Dominator Colorings in Graphs'. Together they form a unique fingerprint.

Cite this