Kazhdan's Property (T) for Graphs
Abstract
D. A. Kahzdan first put forth property (T) in relation to the study of discrete subgroups of Lie groups of finite covolume. Through a combinatorial approach, we define an analogue of property (T) for regular graphs. We then prove the basic combinatorial and metric properties of Kazhdan groups in this context. In particular, we use our methods to construct infinite families of expanders as in the classical case. Finally, we consider the combinatorial analogue of the group theoretic property $(\tau)$ and prove its basic properties.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2006
 arXiv:
 arXiv:math/0607351
 Bibcode:
 2006math......7351B
 Keywords:

 Mathematics  Combinatorics;
 05C25
 EPrint:
 13 pages