@inbook{37c7454041674513a006cfdfeb53d1e7,

title = "Dominator and Total Dominator Colorings in Graphs",

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.",

keywords = "Domination, Dominator coloring, Graph colorings, Total dominator coloring",

author = "Henning, {Michael A.}",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-58892-2_5",

language = "English",

series = "Developments in Mathematics",

publisher = "Springer",

pages = "101--133",

booktitle = "Developments in Mathematics",

address = "Germany",

}