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A unified approach to the incidence graphs of (weak) generalized quadrangles | ||
Journal of Discrete Mathematics and Its Applications | ||
دوره 9، شماره 1، 2024، صفحه 65-72 اصل مقاله (245.92 K) | ||
نوع مقاله: Full Length Article | ||
شناسه دیجیتال (DOI): 10.22061/jdma.2024.10798.1070 | ||
نویسندگان | ||
Sezer Sorgun* 1؛ Ali Gökhan Ertaş2 | ||
1Nevşehir Hacı Bektaş Veli University | ||
2Kütahya Dumlupınar University | ||
تاریخ دریافت: 14 فروردین 1403، تاریخ بازنگری: 26 فروردین 1403، تاریخ پذیرش: 17 تیر 1403 | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Generalized quadrangles؛ Finite Geometries؛ Bipartite Graphs | ||
مراجع | ||
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