Adjacent Vertex Reducible Vertex-Total Coloring of Graphs

Let G =( V, E) be a simple graph,k (1 ≤ k ≤ Δ(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 vertextotal chromatic number of G, simply denoted by χavrvt(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.