图 P2×Cn的均匀邻强边色数

摘要

对图G(V,E),一正常边染色f若满足:(1)对(V)uv∈E(G),f[u]≠f[v],其中f[u]={f(uv)|uv∈E};(2)对任意i≠j,有||E|-|Ej||≤1,其中Ei={e| e∈E(G)且f(e)=i}.则称f为G(V,E)的一k-均匀邻强边染色,简称k-EASC,并且称Xcas(G)=min{k|存在G(V,E)的一k-EASC为G(V,E)的均匀邻强边色数.本文得到了图P2×Cn的均匀邻强边色数.%Let G(V,E) be a simple connected graph with order not less than 3. A proper k-edge coloring f of G(V,E) be called a k-equitable adjacent strong edge coloring, be abbreviatted a k-ASEC, of G(V,E) iff every uv ∈ E (C) have f[u]≠ f[v] and || Ei] - |Ej|| ≤1, where f[x]= {f(wx) |wx ∈ E (G) }, f (ux) is the color of edge wx∈E(G), and Ek= {e|e∈E(G) and f(e)=k}; and Xcax(G)=min{k |there is a k-EASEC of G} be called the equitable adjacent strong edge chromatics number of G(V,E). In this paper, we present some results about equitable adjacent strong edge chromatics number of graph P2 ×Cn.