Neighbor Sum Distinguishing Total Colorings of Graphs with Bounded Maximum Degree and Maximum Average Degree
Baojian Qiu, Jihui Wang, Yan Liu, Zhenyu Xu · 2017
A total k-coloring c of G is called k-neighbor sum distinguishing if for each edge uv, the sum of color of u and the colors of its incident edges is different from the sum of color of v and the colors of its incident edges. The smallest k is called the neighbor sum distinguishing total chromatic number. and first introduced this coloring and conjectured that the neighbor sum distinguishing total chromatic number of G is less than or equal to maximum degree of G add 3 for any simple graph. By using the Combinatorial Nullstellensatz and the discharging method, we prove that the conjecture holds for graphs with maximum degree at least 8 and maximum average degree less than 4.5.