On fuzzy dominator coloring in fuzzy graphs
R. Jahir Hussain, K. S. Kanzul Fathima · Applied Mathematical Sciences · 2015
In this paper, a new concept of fuzzy dominator coloring is introduced. Fuzzy dominator chromatic number of fuzzy complete graph, fuzzy complete bipartite graph, and fuzzy cycle has been discussed. Bounds for fuzzy dominator chromatic number and necessary and sufficient condition for fuzzy dominator chromatic number to be 2 and n has been found. It is proved that fuzzy dominator chromatic number equals fuzzy chromatic number if at least one node of G has strong degree n-1.