关于D(F_n)和D(W_n)的点关联邻点可区别全色数

On the Vertex Incidence-adjacent Vertex-distinguishing Total Coloring of D(F_n) and D(W_n)

对简单图G(V,E),f是从V(G)∪E(G)到{1,2,…,k}的映射,k是自然数,若满足:1)uv,uω-∈E(G),v≠,-ωf(uv)≠f (uω-);2)uv∈E G,C(u)≠C(v).则称f是G的点关联邻点可区别全染色法,其所用到的最少颜色数称为图G的点关联邻点可区别全色数.这里C(u)=f(u)∪f(uv)uv∈E(G).得到了扇和轮的倍图的点关联邻点可区别全色数.

Let G be a simple graph, k is a positive integer, f is a mapping from V（G）∪E（G） to {1,2,…,k} such that A↓uv.∈E（G） , then A↓uv.uω ∈E（G）,v≠,-ωf（uv）≠f （uω-）; A↓uv∈E G,C（u）≠C（v）, we say that fis the vertex incidence-adjacent vertex distinguishing total coloring of G. The minimal number of k is called the vertex incidence-adjacent vertex distinguishing total chromatic number of G, whereC（u） = {f（u） } ∪{f（uv） [uv∈ E（G） }. In this paper, we discuss the vertex incidence-adjacent vertex distinguishing total chromatic number of the double graph of Fan and Wheel.