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: https://doi.org/10.1016/j.disc.2017.02.016

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.

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