Some Diameter Notions of the Generalized Mycielskian of a Graph

Gamma coloring of Mycielskian graphs

“…Let C be a proper coloring of a graph G. A subset U of V(G) is said to be C-colorful if every vertex of U receives different color under the coloring C. A subset U of V(G) is said to be color transversal with respect to the coloring C if U intersects every color class of the coloring C. The study of a graph theoretical parameter in Mycielskian construction of graphs is one of the interesting research fields in graph theory. Some of such studies are Dominator coloring of Mycielskian graphs (1) , strong coloring of Mycielskian graphs (2) , connectivity of Mycielskian graphs (3,4) , packing coloring of Mycielskian graphs (5) , total chromatic number of Mycielskian graphs (6) , diameter of Mycielskian of graphs (7) , total weight choosability of Mycielskian graphs (8) and Hamilton-connected Mycielskian graphs (9,10) . In this paper we define the notion of gamma coloring and discuss about gamma coloring of Mycielskian graphs.…”