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

Document Type : Full Length Article

Authors

1 Nevşehir Hacı Bektaş Veli University

2 Kütahya Dumlupınar University

Abstract

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.

Keywords

Main Subjects


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Volume 9, Issue 1
Special Issue of the IGTC 16
2024
Pages 65-72
  • Receive Date: 02 April 2024
  • Revise Date: 14 April 2024
  • Accept Date: 07 July 2024
  • Publish Date: 01 July 2024