设ｆ：Ｖ（Ｇ）∪Ｅ（Ｇ）→｛１，２，…，ｋ｝是简单图Ｇ的一个正常ｋ-全染色．令Ｃ（ｆ，ｕ）＝｛ｆ（ｅ）：ｅ∈Ｎ（ｕ）｝，ｅＣ［ｆ，ｕ］＝Ｃ（ｆ，ｕ）∪｛ｆ（ｕ）｝，Ｃ［ｆ，ｕ］＝Ｃ（ｆ，ｕ）∪｛ｆ（ｘ）：ｘ∈Ｎ（ｕ）｝∪｛ｆ（ｕ）｝．Ｎ（ｕ）表示顶点ｕ的邻集，Ｎ（ｕ）２ｅ表示与顶点ｕ的相关联的边集合．令Ｃ［ｆ；ｘ］＝｛Ｃ（ｆ，ｘ）；Ｃ［ｆ，ｘ］；Ｃ［ｆ，ｘ］｝，对任意的边ｘｙ∈Ｅ（Ｇ），Ｃ［ｆ；ｘ］２≠Ｃ［ｆ；ｙ］表示Ｃ（ｆ，ｘ）≠Ｃ（ｆ，ｙ），Ｃ［ｆ，ｘ］≠Ｃ［ｆ，ｙ］，Ｃ［ｆ，ｘ］≠Ｃ［ｆ，ｙ］同时成立．对任意的边ｘｙ∈Ｅ（Ｇ），２２如果有Ｃ［ｆ；ｘ］≠Ｃ［ｆ；ｙ］成立，则称ｆ是图Ｇ的一个ｋ-（３）-邻点可区别全染色（简记为ｋ-（３）-ＡＶＤＴＣ）．图Ｇ的（３）-邻点可区别全染色中所需最少的颜色数叫做Ｇ的（３）-邻点可区别全色数，记为″（Ｇ）．文章研究（２，（３）ａｓ２）-递归极大平面图的（３）-邻点可区别全染色，并确定此类图的（３）-邻点可区别全色数．此外，提出了简单图的（３）-邻点可区别全染色猜想．

Letf: V(G)UE(G)-→{1,2,-,k} be a proper k-total coloring of a simple graph G. Set C(f,u) = {f(e): e∈N.(u)}, C[f,u] =C(f,u)∪{f(u)}, G2[f,u]=C(f,u)∪{f(x): x∈N(u)}∪{f(u)}. Sup- pose C[f; x]= C(f, x);C[f, x];C2[f, x]}. For each edge ry∈E(G) ,C[f;x]≠C[f;y] denotes C(f,x) ≠C(f,y) ,C[f,x]≠C[f,y],C2[f,x]≠C[f,y] holding at the same time. We callf to be a k-(3)-adjacent vertex distinguishing total coloring (k-(3)-AVDTC for short) of G if C[f;x]≠C[f;y] for each edge xy∈ E(G). The minimum number of k colors required for which G admits ak-(3)-AVDTC is denoted by x"3)w(G), and called the (3)-AVDTC chromatic number of G. In this paper, we investigate (3 )-adjacent vertex distin- guishing total coloring of(2 ,2 )-recursive maximal planar graphs and their ( 3)-AVDTC chromatic numbers are determined. Moreover, we propose a conjecture on (3 ) -adjacent vertex distinguishing total colorings of simple graphs.