A combinatorial algorithm to optimally colour the edges of the graphs that are join of regular graphs

We prove that the edges of every even graph G = G1 + G2 that is the join of two regular graphs Gi = (Vi,Ei) can be coloured with (G) colours, whenever (G) = (G2) + |V (G1)|. The proof of this result yields a combinatorial algorithm to optimally colour the edges of this type of graphs.