  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.
