Adjacent-vertex-distinguishing Total Coloring on 2-connected Outer Plane Graph with△(G)=6

let G be a simple connetced graph,a k-proper total coloring of G is called adjacent-vertex-distinguishing if for arbitrary two adjacent vertices u and v,we haveC(u)≠ C(v),whereC(u) is the set of the colors of u and edges which is adjacent to u.Such is the minimum if that G has a k-adjacent-vertex-distinguishing total coloring is called the adjacent vertex distinguishing total chromatic number.the adjacent-vertex-distinguishing total chromatic numbers on 2-connetced outer plane graphy with△(G)=6 are given in this paper.