Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cactus Trees, and Estimations of the Spectral Radius of
  Vertex-Transitive Graphs   This paper gives lower bounds on the spectral radius of vertex-transitive
graphs, based on the number of ``prime cycles'' at a vertex. The bounds are
obtained by constructing circuits in the graph that resemble ``cactus trees'',
and enumerating them. Counting these circuits gives a coefficient-wise
underestimation of the Green function of the graph, and hence and
underestimation of its spectral radius.
  The bounds obtained are very good for the Cayley graph of surface groups of
genus g>=2, with standard generators (these graphs are the 1-skeletons of
tessellations of hyperbolic plane by 4g-gons, 4g per vertex). We have for
example for g=2
  0.662420<=|M|<=0.662816, and for g=3
  0.552773<=|M|<=0.552792.

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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics