On The Total Dominator Edge Chromatic Number

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 somecolorclass. Thetotaldominatoredgechromaticnumber(brieflyTDECnumber)χ′t d(G)ofGistheminimumnumberofcolorclassesinaTDE-coloring of G. We obtain some properties of χ′t d(G) and compute this parameter for specific graphs. We also examine the effects on χ′t d(G) when G is modified by operations on vertex and edge of G