Total dominator chromatic number of some operations on a graph

Abstract

Let $G$ be a simple graph. A total dominator coloring of $G$ is a proper coloring of the vertices of $G$ in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number ${\chi }_d^t(G)$ of $G$ is the minimum number of colors among all total dominator coloring of $G$. In this paper, we examine the effects on ${\chi }_d^t(G)$ when $G$ is modified by operations on vertex and edge of $G$.

10 pages, 5 figures. arXiv admin note: text overlap with arXiv:1511.01652

Cited by in corpus (3)

• Dominated chromatic number of some operations on a graph
• On the dominated chromatic number of certain graphs
• Effects of Some Operations on Domination Chromatic Number in Graphs