论文标题
在一组顶点的度量尺寸上
On the Metric Dimensions for Sets of Vertices
论文作者
论文摘要
最初设计的分辨集是为了一次定位图的顶点。为了同时定位图的多个顶点，最近引入了$ \ {\ ell \} $ - 分辨集集。在本文中，我们介绍了有关图形的$ \ {\ ell \} $的新结果。除了证明一般结果外，我们还考虑了$ \ {2 \} $ - 在Rook的图中解析集，并将它们连接到块设计。我们还介绍了$ \ ell $ -solid解析集的概念，这是对固体分解集的自然概括。我们证明了一些$ \ ell $ -solid -solid-resolving集的一般界限和特征，并展示了$ \ ell $ -solid-和$ \ {\ ell \} $ - 分辨率 - 分辨率相互连接。在本文的最后一部分中，我们专注于无限的花sn蛇家族。我们考虑$ \ ell $ -solid-和$ \ {\ ell \} $ - 花snarks的度量尺寸。在有关花sn的两个证据中，我们使用了一种新的计算机辅助还原式方法。
Resolving sets were originally designed to locate vertices of a graph one at a time. For the purpose of locating multiple vertices of the graph simultaneously, $\{\ell\}$-resolving sets were recently introduced. In this paper, we present new results regarding the $\{\ell\}$-resolving sets of a graph. In addition to proving general results, we consider $\{2\}$-resolving sets in rook's graphs and connect them to block designs. We also introduce the concept of $\ell$-solid-resolving sets, which is a natural generalisation of solid-resolving sets. We prove some general bounds and characterisations for $\ell$-solid-resolving sets and show how $\ell$-solid- and $\{\ell\}$-resolving sets are connected to each other. In the last part of the paper, we focus on the infinite graph family of flower snarks. We consider the $\ell$-solid- and $\{\ell\}$-metric dimensions of flower snarks. In two proofs regarding flower snarks, we use a new computer-aided reduction-like approach.
