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.
Sorgun, S., & Gökhan Ertaş, A. (2024). A unified approach to the incidence graphs of (weak) generalized quadrangles. Journal of Discrete Mathematics and Its Applications, 9(1), 65-72. doi: 10.22061/jdma.2024.10798.1070
MLA
Sezer Sorgun; Ali Gökhan Ertaş. "A unified approach to the incidence graphs of (weak) generalized quadrangles". Journal of Discrete Mathematics and Its Applications, 9, 1, 2024, 65-72. doi: 10.22061/jdma.2024.10798.1070
HARVARD
Sorgun, S., Gökhan Ertaş, A. (2024). 'A unified approach to the incidence graphs of (weak) generalized quadrangles', Journal of Discrete Mathematics and Its Applications, 9(1), pp. 65-72. doi: 10.22061/jdma.2024.10798.1070
VANCOUVER
Sorgun, S., Gökhan Ertaş, A. A unified approach to the incidence graphs of (weak) generalized quadrangles. Journal of Discrete Mathematics and Its Applications, 2024; 9(1): 65-72. doi: 10.22061/jdma.2024.10798.1070
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