完全立方Halin图的2-距离着色

2-Distance Coloring of Complete Cubic Halin Graphs

图G的2-距离着色是正常的顶点着色,并且使G中距离不大于2的任意两个顶点着不同的颜色.图G的2-距离色数是图G的所有2-距离着色中所用色数的最小者,记为χ2d(G).探讨了完全立方Halin图Hn的2-距离着色,并得χ2d(H0)=4,5≤χ2d(Hn)≤6(n≥1).

The 2 - distance coloring of a graph G is a proper coloring such that no two vertices at distance less than or equal to 2 in Gare assigned the same color. The 2 - distance chromatic number of a graph G, denoted by X2d ≤（G） , is the smallest integer k for which G admits a star coloring with k colors. In this paper, we show that if Hn is a complete cubic Halin graph, then 5 ≤X2d （ Hn ）≤6 （ n≥1 ）.