Abstract:

A proper total coloring of a simple graph G is called vertex distinguishing if for any two distinct vertices u and v in G, the set of colors assigned to the elements incident to u differs from the set of colors incident to v.  The minimal number of colors required for a vertex distinguishing total coloring of G is called the vertex distinguishing total coloring chromatic number. The vertex distinguishing total chromatic number of some complement double graphs is obtained.

Key words: vertex distinguishing total coloring; vertex distinguishing total chromatic number; complement double graph