Kesern图的邻强边着色

Adjacent Strong Edge Chromatic Number of Kesern Graphs

设图G(V,E)为简单图,其点数不小于3.则其邻强边染色是指对于图G(V,E),若σ:E→{1,2,…,n}为其一正常着色, u,v∈V,当uv∈E(G)时,若c(u)≠c(v),其中c(u)={σ(uv)｜uv∈E(G)},则称σ为G的邻强边着色.记χ′as(G)=min{k｜k为G的k-邻强边着色法}.本文将通过特别的方法来记图的染色过程.并通过对图的着色得到以下结果:K(5,2),K(6,2),K(7,2)邻强边色数分别为4,7,11.其中K(m,n)表n个元素中,m元素的Kesern图.

Let G(V,E) be a simple connected graph with order not less than 3.What's adjacent strong edge coloring is meaning that if a proper kedge coloring σ is satisfied with c(u)≠c(v), where c(u)={σ(uv)|uv∈E(G)}, then σ is called kadjacent strong edge coloring of G. In the paper, we use special method to remember the process of the coloring of graph. We define: χ′as(G)=min{k|k is the kadjacent strong edge coloring of G}. And through the coloring of graph, we get the following results: the adjacent strong coloring of K(5,2),K(6,2) and K(7,2) are their own 4,7,11.