Introduction to total dominator edge chromatic number
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Original versionTWMS Journal of Applied and Engineering Mathematics. 2022, 12 (3), 786-798.
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) χt d(G) of G is the minimum number of color classes in a TDE-coloring of G. We obtain some properties of χt d(G) and compute this parameter for specific graphs. We examine the effects on χt d(G) when G is modified by operations on vertices and edges of G. Finally, we consider the k-subdivison of G and study TDEC-number of this kind of graphs.