论文标题
直径图图2的定位数和度量尺寸
The localization number and metric dimension of graphs of diameter 2
论文作者
论文摘要
我们考虑某些直径图$ 2 $的定位号和度量尺寸，重点是没有4个循环的Kneser图和图。对于直径$ 2 $的旋塞图，我们找到了本地化编号和度量尺寸的上限和下限，并且在许多情况下，这些参数仅通过加成常数而不同。我们对旋塞图的度量尺寸的结果对早期图表有所改善，在无限的许多情况下产生了精确的值。我们确定直径$ 2 $和极性图的摩尔图的本地化编号和度量尺寸的界限。
We consider the localization number and metric dimension of certain graphs of diameter $2$, focusing on families of Kneser graphs and graphs without 4-cycles. For the Kneser graphs with diameter $2$, we find upper and lower bounds for the localization number and metric dimension, and in many cases these parameters differ only by an additive constant. Our results on the metric dimension of Kneser graphs improve on earlier ones, yielding exact values in infinitely many cases. We determine bounds on the localization number and metric dimension of Moore graphs of diameter $2$ and polarity graphs.
