Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic characterizations of regularity properties in bipartite graphs   Regular and distance-regular characterizations of general graphs are
well-known. In particular, the spectral excess theorem states that a connected
graph G is distance-regular if and only if its spectral excess (a number that
can be computed from the spectrum) equals the average excess (the mean of the
numbers of vertices at extremal distance from every vertex). The aim of this
paper is to derive new characterizations of regularity and distance-regularity
for the more restricted family of bipartite graphs. In this case, some
characterizations of (bi)regular bipartite graphs are given in terms of the
mean degrees in every partite set and the Hoffman polynomial. Moreover, it is
shown that the conditions for having distance-regularity in such graphs can be
relaxed when compared with general graphs. Finally, a new version of the
spectral excess theorem for bipartite graphs is presented.

24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat