On bipartite biregular large graphs

A bipartite graph G=(V,E) with V=V_1∪ V_2 is biregular if all the vertices of each stable set, V_1 and V_2, have the same degree, r and s, respectively. This paper studies difference sets derived from both Abelian and non-Abelian groups. From them, we propose some constructions of bipartite biregular graphs with diameter d=3 and asymptotically optimal order for given degrees r and s. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound.