Total dominator chromatic number of some operations on a graph

2016/06/02 by Nima Ghanbari, Ghanbari, Nima, ‎Saeid Alikhani +1
Computer Science · Mathematics · #05C15 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1606.00666

openalex publication_date 2016/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 χ_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 χ_d^t(G) when G is modified by operations on vertex and edge of G.

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