English

Total dominator coloring of central graphs

Combinatorics 2018-05-09 v3

Abstract

A total dominator coloring of a graph GG is a proper coloring of GG in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number of a graph is the minimum number of color classes in a total dominator coloring of it. Here, we study the total dominator coloring on central graphs by giving some tight bounds for the total dominator chromatic number of the central of a graph, join of two graphs and Nordhaus-Gaddum-like relations. Also we will calculate the total dominator chromatic number of the central of a path, a cycle, a wheel, a complete graph and a complete multipartite graph.

Keywords

Cite

@article{arxiv.1801.05137,
  title  = {Total dominator coloring of central graphs},
  author = {Farshad Kazemnejad and Adel P. Kazemi},
  journal= {arXiv preprint arXiv:1801.05137},
  year   = {2018}
}
R2 v1 2026-06-22T23:46:20.733Z