Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kazhdan's Property (T) for Graphs   D. A. Kahzdan first put forth property (T) in relation to the study of
discrete subgroups of Lie groups of finite co-volume. 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.

19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph