小运动顶点传递图与小最小度传递置换群

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2025-05-22 DOI:10.1016/j.jcta.2025.106065

Antonio Montero , Primož Potočnik

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引用次数: 0

摘要

图的运动是由非平凡自同构移动的顶点的最小数量。等价地，它可以被定义为它的自同构群的最小度（作为顶点上的置换群）。本文给出了小极小度置换群（原群和非原群）的一些结果。根据这些结果，我们对运动为4或素数的顶点传递图进行了分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree

The motion of a graph is the minimum number of vertices that are moved by a non-trivial automorphism. Equivalently, it can be defined as the minimal degree of its automorphism group (as a permutation group on the vertices). In this paper, we develop some results on permutation groups (primitive and imprimitive) with small minimal degree. As a consequence of such results, we classify vertex-transitive graphs whose motion is 4 or a prime number.

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.