{"title":"具有非平凡自同构参数(37,18,8,9)的强正则图","authors":"D. Crnković, Marija Maksimović","doi":"10.26493/2590-9770.1295.25b","DOIUrl":null,"url":null,"abstract":"All strongly regular graphs having at most 36 vetrices have been enumerated. Hence, the first open case is enumeration of the SRGs with parameters (37,18,8,9). In this paper we show that there are exactly forty SRGs with parameters (37,18,8,9) having nontrivial automorphisms. Comparing the constructed graphs with previously known SRGs with these parameters we conclude that six of the SRGs with parameters (37,18,8,9) constructed in this paper are new, and that up to isomorphism there are at least 6766 strongly regular graphs with parameters (37,18,8,9).","PeriodicalId":236892,"journal":{"name":"Art Discret. Appl. Math.","volume":"48 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Strongly regular graphs with parameters (37, 18, 8, 9) having nontrivial automorphisms\",\"authors\":\"D. Crnković, Marija Maksimović\",\"doi\":\"10.26493/2590-9770.1295.25b\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"All strongly regular graphs having at most 36 vetrices have been enumerated. Hence, the first open case is enumeration of the SRGs with parameters (37,18,8,9). In this paper we show that there are exactly forty SRGs with parameters (37,18,8,9) having nontrivial automorphisms. Comparing the constructed graphs with previously known SRGs with these parameters we conclude that six of the SRGs with parameters (37,18,8,9) constructed in this paper are new, and that up to isomorphism there are at least 6766 strongly regular graphs with parameters (37,18,8,9).\",\"PeriodicalId\":236892,\"journal\":{\"name\":\"Art Discret. Appl. Math.\",\"volume\":\"48 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Art Discret. Appl. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26493/2590-9770.1295.25b\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Art Discret. Appl. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/2590-9770.1295.25b","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Strongly regular graphs with parameters (37, 18, 8, 9) having nontrivial automorphisms
All strongly regular graphs having at most 36 vetrices have been enumerated. Hence, the first open case is enumeration of the SRGs with parameters (37,18,8,9). In this paper we show that there are exactly forty SRGs with parameters (37,18,8,9) having nontrivial automorphisms. Comparing the constructed graphs with previously known SRGs with these parameters we conclude that six of the SRGs with parameters (37,18,8,9) constructed in this paper are new, and that up to isomorphism there are at least 6766 strongly regular graphs with parameters (37,18,8,9).
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