## On the Spectra of Certain Graphs Arising from Finite Fields |

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### Contents

Terrass Graphs | 14 |

Graphs from GLZp | 25 |

Graphs from GLnp | 81 |

Copyright | |

3 other sections not shown

### Common terms and phrases

1-dimensional eigenvalues adjacency matrix adjacency operator Aff(p AK(g analogous c-lk Cayley graph cn-i Conjecture construct graphs Corollary corresponding eigenvalue eigenfunctions Eigenvalues of graphs equals the 1-dimensional expander graphs Finite Fields functions Gerhard Ringel girth given Graph Isomorphisms graph theory Graph Type Eigenvalues graph Xp graphs associated graphs from GL(n,p group isomorphism hence higher dimensional eigenvalues induced space irreducible representations Legendre symbol Lemma 15 Lemma 43 Lemma 51 matjk Mj<k mord multiplicative character nonbipartite nonzero normalized eigenvalues notation number of vertices odd prime orthogonal Poincare upper half Proposition 26 Ramanujan bound Ramanujan graphs regular of degree representations of G S,a,c e Sato-Tate set Sp(S,a,c shift matrix sin2 Sp(S subgroup of GL(2,p symmetric symmetric matrix teFpx Terras's graphs Theorem 12 ueFpx upper half plane vertex vertex-transitive Xm(y xn-i Xp(S yeFpx zero