关于图Cn·Cm,Cn·Fm,Cn·Wm的邻强边着色

Adjacent Strong Edge Chromatic Number of Cn·Cm,Cn·Fm,Cn·Wm Graphs

设图G(V,E)为简单图,其点数不小于3.图G(V,E)的k-邻强边染色是指映射f:E(G)→{1,2,…,k},使f为正常边着色,且坌u,v∈V(G),当uv∈E(G)时,有C(u)≠C(v),其中C(u)={f(uv)|uv∈E(G)}.记X'as(G)=m in{k|G有k-邻强边着色法}.称X'as(G)为G的邻强边色数。本文构造了三类图Cn·Cm,Cn·Fm,Cn·W m,通过对图的具体着色得到其邻强边色数分别为4,m+1,m+1.

Let G(V,E) be a simple connected graph with order not less than 3.The adjacent strong edge coloring means that if a proper k-edge coloring f is satisfied with C(u)≠C(v),∨u,v∈V(G) ,if uv∈E(G),Where C(u) ={f(uv) |uv∈E(G) },then f is called k-adjacent strong edge coloring of G. In the paper, we have constructed three types of graphs Cn·Cm,Cn·Fm,Cn·Wm. We define: Xas' (G)=min{k|G has the k-adjacent strong edge coloring }And Xas(G) is called the adjacent strong edge chromatic number of G. we get the adjacent strong edge chromatic numbers of m+1,m+1 and 4, respectively in the paper.