UNIVERSITY OF NORTH FLORIDA & MAYO CLINIC-JAX
11 Feb 2017

The Spectrum of Platonic Graphs over Finite Fields

For q = p, the graph G(q) is called the qth Platonic graph. The name comes from the fact that when p = 3 or 5, the graphs G(p) correspond to 1-skeletons of two of the Platonic solids, in other words, the tetrahedron and the icosahedron as in [2]. More generally, G(p) is the 1-skeleton of a triangulation of the modular curve X(p). In this paper, we determine the spectrum of G(q) and thus generalize results of P.E. Gunnells, “Some elementary Ramanujan graphs”.

with Dominic Lanphier and Marvin Minei, Discrete Math. 307 (2007), no. 9-10, 1074–1081.  DOI: 10.1016/j.disc.2006.07.032   MR2292536 05C25 (05C50) 

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