论文标题
定位$ n $ ary树的颜色数量
The Locating-Chromatic number of an $n$-ary Trees
论文作者
论文摘要
图$ g $的定位颜色数是最小的整数$ n $，因此$ g $具有适当的$ n $颜色$ c $，并且所有顶点对$ c $生成的颜色的距离有不同的距离。我们研究了$ k $ level $ n $ -ary树的定位数量的渐近价值。当$ k $转到无限时，当$ n $转到无限时，这棵树的定位数字的作用非常不同。如果我们修复了$ k \ geq2 $，几乎所有$ n $ -ary tree $ t（n，k）$满足$χ_l（t（n，k））= n+k-1 $;因此，$ \ lim \ limits_ {n \ to \ infty}χ_l（t（n，k）） - n = k-1 $。但是，如果我们修复了$ n \ geq 2 $，则$χ_l（t（n，k））= o（k）$。
The locating-chromatic number of a graph $G$ is the smallest integer $n$, such that $G$ has a proper $n$-coloring $c$ and all vertices have different vectors of distances to the colors generated by $c$. We study the asymptotic value of the locating-chromatic number of a $k$-level $n$-ary tree. The locating-chromatic number of this tree acts very differently when $k$ goes to infinity and when $n$ goes to infinity. If we fix $k\geq2$, almost all $n$-ary Tree $T(n,k)$ satisfy $χ_L(T(n,k))=n+k-1$; so $\lim\limits_{n\to \infty} χ_L(T(n,k))-n=k-1$. But if we fix $n\geq 2$, then $χ_L(T(n,k))=o(k)$.
