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 4 and girth 8. In this paper, we investigate the connection between generalized quadrangles and octographic bipartite graph (shortly, 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 O-graph. Also we obtain some properties of 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.