On J-colorability of certain derived graph classes

A vertex v of a given graph G is said to be in a rainbow neighbourhood of G, with respect to a proper coloring C of G, if the closed neighbourhood N[v] of the vertex v consists of at least one vertex from every color class of G with respect to C. A maximal proper coloring of a graph G is a J-coloring of G such that every vertex of G belongs to a rainbow neighbourhood of G. In this paper, we study certain parameters related to J-coloring of certain Mycielski-type graphs.