A unified approach to the incidence graphs of (weak) generalized quadrangles

A generalized quadrangle is a point-line geometry such that the incidence graph is a connected, bipartite graph of diameter ۴ and girth ۸. In this paper, we investigate the connection between generalized quadrangles and octographic bipartite graph (shortly, \mathcal{O}-graph), which are a class of bipartite graphs satisfying certain axioms regarding graph-theoretic properties of them. We prove that every incidence graph of a generalized quadrangle is a \mathcal{O}-graph. Also we obtain some properties of \mathcal{O}-graphs in terms of graph invariants. Finally, we conclude by discussing the implications of our findings and potential avenues for future research in this area.

کلیدواژه ها:

Generalized quadrangles ، Finite Geometries ، bipartite graphs