论文标题
图中心的可能的红衣主教
Possible cardinalities of the center of a graph
论文作者
论文摘要
图的中央顶点是一个顶点，其偏心率等于半径。图的中心是所有中央顶点的集合。图的中心比是其中心与秩序的基数比率。 1982年，巴克利（Buckley）证明，每个不超过一个的正理性数量是某些图的中心比率。在本文中，我们通过确定具有给定顺序和半径的图形中心可以进行哪些基础性来获得更详细的信息。结果中有意外的现象。例如，存在订单$ 14 $和半径$ 6 $的订单图，其中心具有基数$ s $，并且仅当$ s \ in \ in \ in \ {1，2，2，2，3，4，9,10,11,12,14 \}。$我们也证明了相关的唯一性结果。
A central vertex of a graph is a vertex whose eccentricity equals the radius. The center of a graph is the set of all central vertices. The central ratio of a graph is the ratio of the cardinality of its center to its order. In 1982, Buckley proved that every positive rational number not exceeding one is the central ratio of some graph. In this paper, we obtain more detailed information by determining which cardinalities are possible for the center of a graph with given order and radius. There are unexpected phenomena in the results. For example, there exists a graph of order $14$ and radius $6$ whose center has cardinality $s$ if and only if $s\in \{ 1, 2, 3, 4, 9,10,11,12,14\}.$ We also prove a related uniqueness result.
