| Title: | Vertex-transitive graphs with small motion and transitive permutation groups with small minimal degree |
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| Authors: | ID Montero, Antonio (Author)
ID Potočnik, Primož (Author) |
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| Files: |  PDF - Presentation file, download (639,67 KB)
MD5: 92C2BB5F45DFDFE89C058A765EBFB6B1
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0097316525000603
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. |
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| Keywords: | fixity, motion, minimal degree, graphs, permutation groups |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.11.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 30 str. |
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| Numbering: | Vol. 216, [article no.] 106065 |
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| PID: | 20.500.12556/DiRROS-22514  |
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| UDC: | 519.17:512 |
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| ISSN on article: | 0097-3165 |
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| DOI: | 10.1016/j.jcta.2025.106065 |
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| COBISS.SI-ID: | 237036803 |
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| Publication date in DiRROS: | 26.05.2025 |
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| Views: | 633 |
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| Downloads: | 320 |
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| Metadata: |    |
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