Vertex-distinguishing total coloring of some complement double graphs

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.