Adjacent vertex distinguishing total coloring of corona product of graphs

An adjacent vertex distinguishing total k-coloring f of a graph G is a proper total k-coloring of G such that no pair of adjacent vertices has the same color sets, where the color set at a vertex v, CfG(v), is {f(v)} ∪ {f(vu)|u ∈ V(G), vu ∈ E(G)}. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph G has adjacent vertex distinguishing total (Δ(G) + 3)-coloring. In this paper we confirm the conjecture for many types of coronas, in particular for generalized, simple and l-coronas of graphs, not relating the results to particular graph classes of the factors.