Abstract: In order to study the conjecture of neighbor sum distinguishing total chromatic number, the structure of minimal counter example graphs is analyzed using the Combinatorial Nullstellensatz and proved that the neighbor sum distinguishing total chromatic number of IC-planar graphs with the maximum degree Δ>=8 without intersecting triangles does not exceed Δ+3 by the discharging method. The research results indicate that the conjecture of neighbor sum distinguishing total chromatic number holds on this class graphs.

Key words: IC-planar graphs, combinatorial nullstellensatz, neighbor sum distinguishing total chromatic number, discharging method