A unified approach to the incidence graphs of (weak) generalized quadrangles
نویسندگان
1 Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Nevşehir 50300, Turkey
2 Department of Informatics, Kutahya Dumlupinar University, Kutahya, 43020, Turkey
doi
10.22061/jdma.2024.10798.1070چکیده
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, $\mathcal{O}$-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.
