Ramanujan type graphs and bigraphs

Cristina M. Ballantine

doi:10.3934/proc.2003.2003.78

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2003, Volume 2003: 78-82. Doi: 10.3934/proc.2003.2003.78 open access

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Ramanujan type graphs and bigraphs

Cristina M. Ballantine^1,

1.
Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01609

Received: July 31, 2002

Revised: February 28, 2003

Published: March 2003

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Abstract

We show that quotients of the Bruhat-Tits building of S$L_3(mathbb(Q)_p)$ form an infinite family of graphs which are Ramanujan type. We investigate the Bruhat-Tits tree associated with U$_3(mathbb(Q)_p)$ and show how its relation to the building of S$L_3(mathbb(Q)_p)$should lead to an estimation of its spectrum.

Keywords:

Hecke operators,
Buildings.

Mathematics Subject Classification: Primary: 11F25; Secondary: 20F32.

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