Equitable total coloring of corona of cubic graphs

The minimum number of total independent sets of V ∪ E of graph G(V,E) is called the total chromatic number of G, denoted by χ′′(G). If difference of cardinalities of any two total independent sets is at most one, then the minimum number of total independent partition sets of V ∪E is called the equitable total chromatic number, and denoted by χ′′ =(G). In this paper we consider equitable total coloring of corona of cubic graphs, G ◦ H. It turns out that, independly on equitable total chromatic numbers of G and H, equitable total chromatic number of corona G ◦ H is equal to ∆(G ◦H) + 1. Thereby, we confirm TCC and ETCC conjectures for coronas of cubic graphs. As a direct consequence we get that all coronas of cubic graphs are of Type 1.