Vertex-minimal graphs with nonabelian $${\mathbf{2}}$$-group symmetry
| Autor: | L.-K. Lauderdale, Jay Zimmerman |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Finite group
Automorphism group Algebra and Number Theory 010102 general mathematics 0102 computer and information sciences 01 natural sciences Graph Subject matter Vertex (geometry) Combinatorics 010201 computation theory & mathematics Discrete Mathematics and Combinatorics 0101 mathematics 2-group Mathematics |
| Zdroj: | Journal of Algebraic Combinatorics. 54:205-221 |
| ISSN: | 1572-9192 0925-9899 |
| DOI: | 10.1007/s10801-020-00975-y |
| Popis: | A graph whose full automorphism group is isomorphic to a finite group G is called a G-graph, and we let $$\alpha (G)$$ denote the minimal number of vertices among all G-graphs. The value of $$\alpha (G)$$ has been established for numerous infinite families of groups. In this article, we expand upon the subject matter of vertex-minimal G-graphs by computing the value of $$\alpha (G)$$ when G is isomorphic to either a quasi-dihedral group or a quasi-abelian group. These results completely establish the value of $$\alpha (G)$$ when G is a member of one of the six infinite families of 2-groups that contain a cyclic subgroup of index 2. |
| Databáze: | OpenAIRE |
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