On the Construction of Generalized Quadrangles as Coset Graphs over Quasigroups with Identity

摘要

A generalized quadrangle is a bipartite graph of diameter 4 and girth 8 with each vertex of degree at least 3. Alternatively, it is a projective geometry in which two distinct points determine at most one line, two distinct lines determine at most one point, and no triangles exist. In this paper, we show that generalized quadrangles may be constructed as coset graphs over quasigroups with identity.