具有大固定性的顶点原始数图

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-04-12 DOI:10.1007/s10231-024-01447-x

Marco Barbieri, Primož Potočnik

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引用次数: 0

摘要

一个数图 \(\Gamma \)的相对固定性被定义为由\(\Gamma \)的非小自形变固定的最大顶点数与\(\Gamma \)的顶点数之比。我们描述了相对固定性至少为 \(\frac{1}{3}\)的顶点-顶点图的特征，并证明了只有有限多个顶点-顶点图具有有界的出值和超过正常数的相对固定性。

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Vertex-primitive digraphs with large fixity

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.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

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.