Finite Regular {0,1}-bigraphs

A {0,1}- bigraph is a connected bigraph with the property that any two distinct vertices have exactly one common neighbour or none at all. If any two distinct vertices of a part P of G have exactly one common neighbour, the part P is called {1}-part. In this paper, basic properties of finite regular {0,1}- bigraphs with at least one {1}-part are studied and some characterization results are given.