Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy equivalence of isospectral graphs   In this paper, we investigate the Quillen model structure defined by Bisson
and Tsemo in the category of directed graphs Gph. In particular, we give a
precise description of the homotopy category of graphs associated to this model
structure. We endow the categories of N-sets and Z-sets with related model
structures, and show that their homotopy categories are Quillen equivalent to
the homotopy category Ho(Gph). This enables us to show that Ho(Gph) is
equivalent to the category cZSet of periodic Z-sets, and to show that two
finite directed graphs are almost-isospectral if and only if they are
homotopy-equivalent in our sense.

4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph