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- W2009824588 abstract "Cayley graphs on a subgroup of GL (3, p ), p >3 a prime, are defined and their properties, particularly their spectra, studied. It is shown that these graphs are connected, vertex-transitive, nonbipartite, and regular, and their degrees are computed. The eigenvalues of the corresponding adjacency matrices depend on the representations of the group of vertices. The “1-dimensional” eigenvalues can be completely described, while a portion of the “higher dimensional” eigenfunctions are discrete analogs of Bessel functions. A particular subset of these graphs is conjectured to be Ramanujan and this is verified for over 2000 graphs. These graphs follow a construction used by Terras on a subgroup of GL (2, p ). This method can be extended further to construct graphs using a subgroup of GL ( n, p ) for n ≥4. The 1-dimensional eigenvalues in this case can be expressed in terms of the 1-dimensional eigenvalues of graphs from GL (2, p ) and GL (3, p ); this part of the spectra alone is sufficient to show that for n ≥4, the graphs from GL ( n, p ) are not in general Ramanujan." @default.
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- W2009824588 date "1998-10-01" @default.
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- W2009824588 title "On the Spectra of Certain Graphs Arising from Finite Fields" @default.
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- W2009824588 doi "https://doi.org/10.1006/ffta.1998.0226" @default.
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