Abstract: By using three types of tree coloring algorithms and combinatorial analysis, we completed the neighbor sum distinguishing edge coloring, the neighbor sum distinguishing total coloring and the neighbor full sum distinguishing total coloring of Halin graphs, and proved that the 1-2-3 conjecture and 1-2 conjecture were valid for Halin graphs. The results show that the neighbor full sum distinguishing total chromatic number of Halin graphs is not more than 3.

Key words: 1-2-3 conjecture, 1-2 conjecture, neighbor full sum distinguishing total coloring, Halin graph