A result on the total colouring of powers of cycles

The total chromatic number χ_T(G) is the least number of colours needed to colour the vertices and edges of a graph G such that no incident or adjacent elements (vertices or edges) receive the same colour. The Total Colouring Conjecture (TCC) states that for every simple graph G, χ_T(G)?Δ(G)+2. This work verifies the TCC for powers of cycles even and 2<k<n/2, showing that there exists and can be polynomially constructed a (Δ(G)+2)-total colouring for these graphs.