1. Total Dominator Edge Chromatic Number of Graphs.
- Author
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Minhui Li, Shumin Zhang, Caiyun Wang, and Chengfu Ye
- Subjects
- *
EDGES (Geometry) , *GRAPH coloring , *COLOR - Abstract
Let G be a simple graph with no isolated edge. A total dominator edge coloring (TDEC) of a graph G is a proper edge coloring such that each edge of G is adjacent to every edge of some (other) color class. The total dominator edge chromatic number (TDEC-number) of G is the minimum number of color classes among all total dominator edge colorings of G, denoted by X′td (G). The stability number of TDEC-number of G is the minimum number of vertices whose removal changes the value of X′td (G) and remaining graph is connected. The bondage number of TDEC-number of G is the minimum number of edges whose removal changes the value of X′td (G). In this paper, we establish the lower and upper bounds of the TDEC-number of a graph G, obtain the TDEC-number and the stability and bondage numbers of some graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2021