Vertex-minimal graphs with dihedral symmetry I
| Autor: | Christina Graves, Lindsey-Kay Lauderdale, Stephen J. Graves |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Vertex (graph theory) 010102 general mathematics 0102 computer and information sciences Dihedral angle Dihedral group 01 natural sciences Theoretical Computer Science One-dimensional symmetry group Combinatorics Edge-transitive graph 010201 computation theory & mathematics Discrete Mathematics and Combinatorics 0101 mathematics Dihedral group of order 6 Graph automorphism Prime power Mathematics |
| Zdroj: | Discrete Mathematics. 340:2573-2588 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2017.06.019 |
| Popis: | Let D 2 n denote the dihedral group of order 2 n , where n ≥ 3 . In this article, we build upon the findings of Haggard and McCarthy who, for certain values of n , produced a vertex-minimal graph with dihedral symmetry. Specifically, Haggard considered the situation when n 2 or n is a prime power, and McCarthy investigated the case when n is not divisible by 2 , 3 or 5 . In this article, we assume n is not divisible by 4 and construct a vertex-minimal graph whose automorphism group is isomorphic to D 2 n . |
| Databáze: | OpenAIRE |
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