{"title":"论耶格尔定理。","authors":"J. Balmaceda","doi":"10.2206/KYUSHUMFS.47.391","DOIUrl":null,"url":null,"abstract":"We give a short and alternative proof of a theorem of F. Jaeger that except for Potts models attached to the complete graphs, the only spin models associated with symmetric conference graphs with n ≥ 5 vertices are the pentagon and the lattice graph L2(3) with 9 vertices. The proof avoids Jaeger's use of the classification of strongly regular graphs having strongly regular subconstituents due to P. J. Cameron, J. M. Goethals, and J. J. Seidel.","PeriodicalId":397897,"journal":{"name":"Memoirs of The Faculty of Science, Kyushu University. Series A, Mathematics","volume":"135 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a theorem of Jaeger.\",\"authors\":\"J. Balmaceda\",\"doi\":\"10.2206/KYUSHUMFS.47.391\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a short and alternative proof of a theorem of F. Jaeger that except for Potts models attached to the complete graphs, the only spin models associated with symmetric conference graphs with n ≥ 5 vertices are the pentagon and the lattice graph L2(3) with 9 vertices. The proof avoids Jaeger's use of the classification of strongly regular graphs having strongly regular subconstituents due to P. J. Cameron, J. M. Goethals, and J. J. Seidel.\",\"PeriodicalId\":397897,\"journal\":{\"name\":\"Memoirs of The Faculty of Science, Kyushu University. Series A, Mathematics\",\"volume\":\"135 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-09-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Memoirs of The Faculty of Science, Kyushu University. Series A, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2206/KYUSHUMFS.47.391\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Memoirs of The Faculty of Science, Kyushu University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2206/KYUSHUMFS.47.391","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文给出了F. Jaeger的一个定理的一个简短的替代证明，即除了完全图上的Potts模型外，与n≥5个顶点的对称会议图相关的自旋模型只有五边形和9个顶点的格图L2(3)。这个证明避免了Jaeger对P. J. Cameron, J. M. Goethals和J. J. Seidel所提出的具有强正则子成分的强正则图的分类的使用。
We give a short and alternative proof of a theorem of F. Jaeger that except for Potts models attached to the complete graphs, the only spin models associated with symmetric conference graphs with n ≥ 5 vertices are the pentagon and the lattice graph L2(3) with 9 vertices. The proof avoids Jaeger's use of the classification of strongly regular graphs having strongly regular subconstituents due to P. J. Cameron, J. M. Goethals, and J. J. Seidel.
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