{"title":"具有大固定性的顶点原始数图","authors":"Marco Barbieri, Primož Potočnik","doi":"10.1007/s10231-024-01447-x","DOIUrl":null,"url":null,"abstract":"<div><p>The relative fixity of a digraph <span>\\(\\Gamma \\)</span> is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of <span>\\(\\Gamma \\)</span> and the number of vertices of <span>\\(\\Gamma \\)</span>. We characterize the vertex-primitive digraphs whose relative fixity is at least <span>\\(\\frac{1}{3}\\)</span>, and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01447-x.pdf","citationCount":"0","resultStr":"{\"title\":\"Vertex-primitive digraphs with large fixity\",\"authors\":\"Marco Barbieri, Primož Potočnik\",\"doi\":\"10.1007/s10231-024-01447-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The relative fixity of a digraph <span>\\\\(\\\\Gamma \\\\)</span> is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of <span>\\\\(\\\\Gamma \\\\)</span> and the number of vertices of <span>\\\\(\\\\Gamma \\\\)</span>. We characterize the vertex-primitive digraphs whose relative fixity is at least <span>\\\\(\\\\frac{1}{3}\\\\)</span>, and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant.</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10231-024-01447-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10231-024-01447-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-024-01447-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The relative fixity of a digraph \(\Gamma \) is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of \(\Gamma \) and the number of vertices of \(\Gamma \). We characterize the vertex-primitive digraphs whose relative fixity is at least \(\frac{1}{3}\), and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant.
期刊介绍:
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.