Generalized quadrangle

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This term is related to: incidence geometry
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Template:Incidence structure property

Definition

A generalized quadrangle is an incidence structure satisfying the following:

  • It is a partial plane, viz, given any two points, there is at most one line through both of them
  • Given a point and a line that are not incident, there is a unique point on that line collinear with the given point (by collinear we mean that there is a line incident to both)

Facts

Point graph

Define the point graph of a generalized quadrangle as follows. The vertices of the graph are the points, and two vertices are adjacent if the corresponding points are collinear. It turns out that the point graph of a generalized quadrangle of type (s,t) is a strongly regular graph with parameters:

References

Algebraic graph theory by Chris Godsil and Gordon Royle, Section 10.8