Spreads in Strongly Regular Graphs
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- 作者：Willem H. Haemers and Vladimir D. Tonchev
- 关键词：strongly regular graphs ; graph colorings ; partial geometries ; spreads ; linked designs ; regular 2 ; graphs
- 刊名：Designs ; Codes and Cryptography
- 出版时间：1996
- 出版年：1996
- 期刊代码：32_09251022
- 类别：bio
- 卷：8
- 期：1/2
- 页码：-
- 数据来源：sp
摘要
A spread of a strongly regular graph is a partitionof the vertex set into cliques that meet Delsarte's bound (alsocalled Hoffman's bound). Such spreads give rise to coloringsmeeting Hoffman's lower bound for the chromatic number and tocertain imprimitive three-class association schemes. These correspondenceslead to conditions for existence. Most examples come from spreadsand fans in (partial) geometries. We give other examples, includinga spread in the McLaughlin graph. For strongly regular graphsrelated to regular two-graphs, spreads give lower bounds forthe number of non-isomorphic strongly regular graphs in the switchingclass of the regular two-graph.