Vertex-minimal planar graphs with cyclic 2-group symmetry
| Autor: | Charles Schmidt, L.-K. Lauderdale, Kassie Archer, Phung T. Tran, Rebecca Darby, Asa Linson, Mariah K. Maxfield |
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| Rok vydání: | 2020 |
| Předmět: |
Vertex (graph theory)
Automorphism group Algebra and Number Theory Conjecture 010102 general mathematics Cyclic group 0102 computer and information sciences Automorphism 01 natural sciences Planar graph Combinatorics symbols.namesake 010201 computation theory & mathematics symbols Discrete Mathematics and Combinatorics 0101 mathematics 2-group Mathematics |
| Zdroj: | Journal of Algebraic Combinatorics. 54:1-15 |
| ISSN: | 1572-9192 0925-9899 |
| DOI: | 10.1007/s10801-020-00964-1 |
| Popis: | For the positive integer m, let $${\mathbb {Z}}_m$$ denote the cyclic group of order m. Vertex-minimal planar graphs with prescribed automorphism group $${\mathbb {Z}}_m$$ were first considered by Marusic. In particular, when m is odd he produced a vertex-minimal planar graph with $${\mathbb {Z}}_m$$ -symmetry. Marusic then conjectured the order of a vertex-minimal planar graph with $${\mathbb {Z}}_m$$ -symmetry when m is a power of 2; in this article, we prove his conjecture. We conclude by discussing vertex-minimal planar graphs with noncyclic automorphism groups and pose some open questions. |
| Databáze: | OpenAIRE |
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