Δ(G)=2的图的孪生强边染色

On Twin Strong Edge Coloring of Graph with Δ(G)=2

设σ是一个阶至少为3的简单连通图G的k-正常边染色,其中颜色集合为{0,1,2,…,k-1}.若对任意距离不超过2的两条边e,,存在σ(e)≠σ(),则称σ为G的强边染色.若图G的强边染色σ能够诱导一个G的2-距离点染色,则称σ是G的孪生强边染色.最少的颜色数为G的孪生强边色数,记为■_(s,t)(G).通过研究简单连通图的孪生强边染色,得到了相应的染色数.

Letσbe a proper k-edge coloring of a simple connected graph G of order at least 3,where the color set is{0,1,2…,k-1}.A proper edge coloring of a graph G is called a strong edge coloring if for any two distinct edges e,e',withd(e,e')≤2,such thatσ(e)≠σ(e').Ifσcan induce a 2-distance vertex coloring of G,thenσis called a twin strong edge coloring of G.The minimum number of colors for which G has a twin strong edge coloring is called the twin strong chromatic index of G,denote byχ's,t(G).In this paper,twin strong edge colorings of simple connected graphs G are studied,and it's twin chromatic number is obtained.