Adjacent-vertex-distinguishing proper total colouring number of ${\bar{K}}_{m}\vee {P}_{n}$

Coloring is a fundamental problem in scientific computation and engineering design. In recent years, a variety of colorings frequently appeared and solved many problems in production. For example, adjacent-vertex-distinguishing proper total coloring, adjacent-vertex-distinguishing proper edge coloring, smarandachely-adjacent-vertex-distinguishing proper edge coloring. It is an important also difficult problem to discuss the coloring numbers of a given graph class. And we focus on the adjacent-vertex-distinguishing proper total coloring numbers in this paper. We study the adjacent-vertex-distinguishing proper total coloring numbers of joint graphs ${\bar{K}}_{m}\vee {P}_{n}.$