f is a mapping from V(G)∪E(G) to {1,2,…,k},then it is called the vertex-edge adjacent vertex-distinguishing total coloring of G if uv∈E(G),f(u)≠f(uv),f(v)≠f(uv),uv∈E(G),C(u)≠C(v),and the minimum number of k is called the vertex-edge adjacent vertex-distinguishing total chromatic number of G,where C(u)={f(u)}∪{f(uv)|uv∈E(G)}.

The chromatic number of adjacent-position distinguishable edge coloring of multi-joined graph S_m∨P_n∨P_n;

Adjacent vertex-distinguishing edge chromatic number of Cm V Kn;