On bipartite graphs of diameter 3 and defect 2

We consider bipartite graphs of degree A<2, diameter D = 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (△,3, -2) -graphs. We prove the uniqueness of the known bipartite (3, 3, -2) -graph and bipartite (4, 3, -2)-graph. We also prove several necessary conditions for the existence of bipartite (△,3, -2) - graphs. The most general of these conditions is that either △ or △-2 must be a perfect square. Furthermore, in some cases for which the condition holds, in particular, when △ = 6 and △ = 9, we prove the non-existence of the corresponding bipartite (△,3,-2)-graphs, thus establishing that there are no bipartite (△,3, -2)-graphs, for 5