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Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree
- Publication Year :
- 2024
-
Abstract
- 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.
- Subjects :
- Mathematics - Combinatorics
Primary:05C25. Secondary: 20B25, 20B10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.10088
- Document Type :
- Working Paper