论文标题
$ n_i $ chromation图的尖锐界限和精确值
Sharp Bounds and Precise Values for the $N_i$-Chromatic Number of Graphs
论文作者
论文摘要
让$ g $是连接的无向图。 $ n_i $ -vertex $ g $。 在本文中，我们分别在其顶点封面号，最高度和直径方面为$ t $ g $的$ t_i（g）$提供了急剧的界限。在某些情况下，我们还确定$ t_i（g）$的精确值。
Let $G$ be a connected undirected graph.~A vertex coloring $f$ of $G$ is an $N_i$-vertex coloring if for each vertex $x$ in $G$, the number of different colors assigned to $N_G(x)$ is at most $i$.~The $N_i$-chromatic number of $G$, denoted by $t_i(G)$, is the maximum number of colors which are used in an $N_i$-vertex coloring of $G$. In this paper, we provide sharp bounds for $t_i(G)$ of a graph $G$ in terms of its vertex cover number, maximum degree and diameter, respectively. We also determine precise values for $t_i(G)$ in some cases.
