Introduction to total dominator edge chromatic number

2018/01/25 by Nima Ghanbari, Ghanbari, Nima, ‎Saeid Alikhani +1
Computer Science · #05C15 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.1801.08871

openalex publication_date 2018/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the total dominator edge chromatic number of a graph G. A total dominator edge coloring (briefly TDE-coloring) of G is a proper edge coloring of G in which each edge of the graph is adjacent to every edge of some color class. The total dominator edge chromatic number (briefly TDEC-number) χ'^t_d(G) of G is the minimum number of color classes in a TDE-coloring of G. We obtain some properties of χ'^t_d(G) and compute this parameter for specific graphs. We examine the effects on χ'^t_d(G) when G is modified by operations on vertex and edge of G. Finally, we consider the k-subdivison of G and study TDEC-number of this kind of graphs.

Related

• Total dominator chromatic number of some operations on a graph
• Total dominator chromatic number of specific graphs
• Total dominator chromatic number of k-subdivision of graphs
• More on the total dominator chromatic number of a graph
• Total dominator total chromatic numbers of cycles and paths