A connected graph is said to be
distance-regular whenever given any two vertices
at path-length distance
apart, the number of
vertices at distance
from
and
from
is a fixed constant (called an
intersection number of the graph) that only depends on
, and not the
vertices
.
The classification of all distance-regular graphs of sufficiently large diameter is an
open problem that, at least for now, seems out of reach. An active area of
research is the classification of distance-regular graphs satisfying certain
additional properties. This paper is motivated by a paper of Miklavič which
found divisibility conditions on the intersection numbers of certain bipartite
-polynomial
distance-regular graphs. We generalize his work to show that the same divisibility
conditions hold for a larger set of bipartite distance-regular graphs.