扇和轮的倍图的点可区别均匀边染色

On Vertex Distinguishing Equitable Edge Coloring of Double Graph of Fan and Wheel

对于简单图G的正常边染色f,若对于u,v∈V(G),有C(u)≠C(v),称f是图G的点可区别边染色,(其中C(u)={f(uv)|uv∈E(G)}).若满足|Ei|-|Ej|≤1(i,j=1,2,…,k),(其中e∈Ei,f(e)=i(i=1,2,…,k)),则称f是图G的点可区别均匀边染色.本文讨论了扇和轮的倍图的点可区别均匀边染色.

A proper edge coloring f of a simple graph G is called vertex distinguishing edge coloring,if any, u,v∈V（G） ,C（u）≠C（v）, （whereC（u） = {f（uv） ｜uv∈E（G）}）. If｜｜Ei｜ - ｜Ej ｜｜≤ 1 （i,j =1,2, …,k）is satisfied, （where any e∈Ei,f（e）=i（i=1,2,…,k））, then f is ealled vertex distinguishing equitable edge col- oring. In this paper, vertex distinguishing equitable edge coloring of double graph of fan and wheel is discussed.