Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smith Normal Form and Acyclic Matrics   An approach, based on the Smith Normal Form, is introduced to study the
spectra of symmetric matrices with a given graph. The approach serves well to
explain how the path cover number (resp. diameter of a tree T) is related to
the maximum multiplicity occurring for an eigenvalue of a symmetric matrix
whose graph is T (resp. the minimum number q(T) of distinct eigenvalues over
the symmetric matrices whose graphs are T). The approach is also applied to a
more general class of connected graphs G, not necessarily trees, in order to
establish a lower bound on q(G).

19
The categories of this paper are: eess
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th