A result on the total colouring of powers of cycles

The total chromatic number χT(G)χT(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  , χT(G)⩽Δ(G)+2χT(G)⩽Δ(G)+2. This work verifies the TCC for powers of cycles Cnk,n even and 2