On the AVDTC of 4-regular graphs

We describe an algorithmic procedure that gives an AVDT-coloring of any 4-regular graph with seven colors. This is a step towards proving the conjecture stating that for any graph G with maximum degree Δ it is χ a ″ ( G ) ≤ Δ + 3 , where χ a ″ ( G ) is the adjacent vertex distinguishing total chromatic number of G .