University of Isfahan Transactions on Combinatorics 2251-8657 4 2 2015 06 01 Total dominator chromatic number of a graph 57 68 6171 10.22108/toc.2015.6171 EN Adel P. Kazemi UMA (University of Mohaghegh Ardabili) Journal Article 2014 04 05 ‎Given a graph $G$‎, ‎the total dominator coloring problem seeks a‎ ‎proper coloring of $G$ with the additional property that every‎ ‎vertex in the graph is adjacent to all vertices of a color class‎. ‎We‎ ‎seek to minimize the number of color classes‎. ‎We initiate to study‎ ‎this problem on several classes of graphs‎, ‎as well as finding‎ ‎general bounds and characterizations‎. ‎We also compare the total‎ ‎dominator chromatic number of a graph with the chromatic number and‎ ‎the total domination number of it‎. https://toc.ui.ac.ir/article_6171_9ef54a03e9ce8be1ddbac6d68cda24c0.pdf