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Archimedean graph designs - II

Forbes, Anthony D.; Griggs, Terry S. and Forbes, Tamsin J. (2017). Archimedean graph designs - II. Discrete Mathematics, 340(7) pp. 1598–1611.

DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.disc.2017.02.016
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Abstract

We examine the design spectra for the vertex–edge 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.

Item Type: Journal Item
Copyright Holders: 2017 Elsevier B.V.
ISSN: 0012-365X
Keywords: graph design; graph decomposition; Archimedean graph
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 56580
Depositing User: Anthony Forbes
Date Deposited: 12 Sep 2018 14:45
Last Modified: 07 Dec 2018 11:11
URI: http://oro.open.ac.uk/id/eprint/56580
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