On dominator coloring of corona products of some generalized graphs

Dominator coloring is a fascinating type of proper coloring where vertices are assigned colors so that every vertex in the graph is within the closed neighborhood of at least one vertex from each color class. The smallest number of colors needed for a dominator coloring is called the dominator chromatic number. In this paper, a new graph product called the closed extended neighborhood corona of two graphs is introduced and its dominator chromatic number for any pair of connected graphs is determined. Also, the dominator chromatic numbers for the extended corona of a path with any graph and a cycle with any graph are derived. Additionally, the dominator chromatic number for the closed neighborhood corona of any two graphs is established.