Pm×Kn的邻点可区别全色数

设G是简单图．设f是一个从V(G)∪E(G)到{1,2,…,k}的映射．对每个v∈V(G),令C_f(v)={f(v)}∪{f(vw)|w∈V(G),vw∈E(G)}．如果f是k-正常全染色,且对任意u,v∈V(G),uv∈E(G),有C_f(u)≠C_f(v),那么称f为图G的邻点可区别全染色(简称为k-AVDTC)．数x_(at)(G)=min{k|G有k-AVDTC}称为图G的邻点可区别全色数．本文给出路P_m和完全图K_n的Cartesion积的邻点可区别全色数．

Adjacent-Vertex-Distinguishing Total Chromatic Number of Pm×Kn

Let G be a simple graph. Let f be a mapping from V(G) ∪E(G) to {1, 2,… ,k}.Let Cf(v) = {f(v)} ∪ {f(vw)|w ∈ V(G),vw ∈ E(G)} for every v ∈ V(G). If f is a k-propertotal-coloring, and if Cf(u) ≠ Cf(v) for u,v ∈ V(G),uv ∈ E(G), then f is called k-adjacentvertex-distinguishing total coloring of G(k-AVDTC of G for short). Let χat(G) = min{k|G has a k-adjacent-vertex-distinguishing total coloring}. Then χat(G) is called the adjacent-vertexdistinguishing total chromatic number. The adjacent-vertex-distinguishing total chromatic number on the Cartesion product of path Pm and complete graph Kn is obtained.