关键词: 单圈图, 正常全染色, 邻点全和可区别全染色, 邻点全和可区别全色数

Abstract: By using structural analysis method, we completely characterized the neighbor full sum distinguishing total coloring of unicyclic graph U, and obtained that ftndi_Σ(U)=Δ(U)+2 when U=C_n and n=0(mod 3),  ftndi_Σ(U)=Δ(U)+1 in other cases. This result  shows that the neighbor full sum distinguishing total coloring conjecture  holds on any unicyclic graph.

Key words: unicyclic graph, proper total coloring,  , neighbor full sum distinguishing total coloring, neighbor full sum distinguishing total chromatic number