Base size, metric dimension and other invariants of groups and graphs
Base size, metric dimension and other invariants of groups and graphs
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DOI：
10.1112/blms/bdq096
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发表时间：
2011-04-01
影响因子：
0.9
通讯作者：
Cameron, Peter J.
中科院分区：
文献类型：
--
作者：
Bailey, Robert F.;Cameron, Peter J.
置换群的基本大小和图的度量维度是群、图、相干配置和关联方案的许多相关参数中的两个。它们在不同的领域被不同的术语反复重新定义，包括计算群论和图同构问题。我们调查了这些参数的许多化身的结果，并为它们提出了一致的术语。我们还提出了一些新的结果，包括产品动作中花环产品的基本尺寸，以及 Johnson 和 Kneser 图的公制尺寸。
The base size of a permutation group, and the metric dimension of a graph, are two of a number of related parameters of groups, graphs, coherent configurations and association schemes. They have been repeatedly redefined with different terminology in various different areas, including computational group theory and the graph isomorphism problem. We survey results on these parameters in their many incarnations, and propose a consistent terminology for them. We also present some new results, including on the base sizes of wreath products in the product action, and on the metric dimension of Johnson and Kneser graphs.