Archimedean graph designs—II
| Autor: | Terry S. Griggs, Tamsin J. Forbes, Anthony D. Forbes |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Truncated cuboctahedron Snub dodecahedron Modulo 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Icosidodecahedron 01 natural sciences Truncated icosahedron Theoretical Computer Science Snub cube Rhombicosidodecahedron Combinatorics 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Truncated dodecahedron Mathematics |
| Zdroj: | Discrete Mathematics. 340:1598-1611 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2017.02.016 |
| Popis: | We examine the design spectra for the vertexedge graphs of some Archimedean solids. In particular, we complete the computation of the spectrum for the truncated cuboctahedron (1 or 64 modulo 144). We extend the known spectrum of the rhombicosidodecahedron by showing that there exist designs of order 81 modulo 240. We add residue class 81 modulo 120 to the known spectra of the icosidodecahedron and the snub cube, each with one possible exception. We add residue class 145 modulo 180 to the known spectra of the truncated dodecahedron and the truncated icosahedron, each with two possible exceptions. Finally, we exhibit the first explicit examples of snub dodecahedron designs. |
| Databáze: | OpenAIRE |
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