Numerical Investigation of the Spectrum for Certain Families of Cayley Graphs

Abstract

In this paper we extend some earlier computations 8]. In particular, the expanding behavior of Cayley graphs of PSL2(F107) is compared with that of the Cayley graphs for the group A10. These computations support the (up to now) unvoiced conjecture of Lubotzky that the symmetric groups and projective linear groups have asymptotically diierent average expanding behavior. We also give a thorough spectral analysis for a natural family of Cayley graphs which does not admit analysis by Selberg's theorem.