D(2)-vertex sum distinguishing total coloring of unicyclic graphs
Let φ be a proper total coloring of graph G,for any u,v ∈ V(G),if dG(u,v)≤2 such that g(u)≠g(v),where g(u)=φ(u)+uω∈E(G)φ(uω),then φ is the 2-distance sum distinguishing total coloring of graph G.The D(2)-vertex sum distinguishing total chromatic numbers χ"2-Σ(G)of graph G is the smallest integer k such that the graph G has a D(2)-vertex sum distinguishing total coloring.This paper fully characterizes the D(2)-vertex sum distinguishing total coloring of unicyclic graphs by using combinatorial nullstellsatz and discharging method,and obtain their the D(2)-vertex sum distinguishing total chromatic numbers.
unicyclic graphtotal-coloringD(2)-vertex sum distinguishing total coloringdis-charging method
万方数据
维普
