Generalized Quadrangle - Graphs

Graphs

There are two interesting graphs that can be obtained from a generalized quadrangle.

• The collinearity graph having as vertices the points of a generalized quadrangle, with the collinear points connected. This graph is a strongly regular graph.
• The incidence graph whose vertices are the points and lines of the generalized quadrangle and two vertices are adjacent if one is a point, the other a line and the point lies on the line. The incidence graph of a generalized quadrangle is characterized by being a connected, bipartite graph with diameter four and girth eight. Incidence graphs of configurations are today generally called Levi graphs, but the original Levi graph was the incidence graph of the GQ(2,2).