图K_(2n)\E(F_m)(n≥4,m≥2)的点可区别边染色

Vertex-distinguishing Edge Coloring of K_(2n)\ E(F_m)(n≥4,m≥2)

对简单图G(V,E),设f是从E(G)到{1,2,…,k}的映射,k为自然数,如果f满足:1)对任意的uv,uw∈E(G),v≠w,有f(uv)≠f(uw);2)对任意的u,v∈V(G),u≠v,有C(u)≠C(v).则称f为图G的k-点可区别边染色法,而最小的k被称为点可区别边色数(其中C(u)={f(uv)|uv∈E(G)}).研究了图K2n\E(Fm)(n≥4,m≥2)的点可区别边色数.

Let G（V,E） be a simple graph,k a positive integer,f a mapping from E（G） to {1,2,…,k} such that：uv,uw∈E（G）,v≠w,f（uv）≠ f（vw）;u,v∈V（G）,C（u）≠C（v）,where C（u）={f（uv）｜uv∈E（G）}.We say that f is a k-vertex distinguishing edge coloring of G,the minimal number k is called the vertex distinguishing edge chromatic number.In this paper,we discuss the vertex distinguishing edge chromatic number of K2n／E（Fm）（n≥ 4,m≥ 2）.