Abstract: We study the D(2)-vertex sum distinguishing total coloring problem of a tricyclic graph with non zero tree height by using analytic method, contradiction method, and the Combinatorial Nullstellensatz, and obtain an upper bound on the D(2)-vertex sum distinguishing total coloring for this type of graphs is Δ(G)+3.

Key words: tricyclic graph, D(2)-vertex sum distinguishing total coloring, D(2)-vertex sum distinguishing total chromatic number