Adjacent Vertex Reducible Vertex-Total Coloring of Graphs

Let G = (V, E) be a simple graph, k (1 ¿ k ¿ ¿(G) +1) is a positive integer, f is a mapping from V(G) ¿ E(G) to {1,2, ···, k} such that ¿uv ¿ E(G),f(u) ¿ f(v) and C(u) = C(v) if d(u) = d(v), we say that f is the adjacent vertex reducible vertex-total coloring of G. The maximum number of k is called the adjacent vertex reducible vertex-total chromatic number of G, simply denoted by ¿_avrvt(G). Where C(u) = {f(u)|u ¿ V(G)} ¿ {f(uv)|uv ¿ E{G)}. In this paper, the adjacent vertex reducible vertex-total chromatic number of some special graphs are given.