• An incidence structure consists of a set of points, a set of lines (disjoint from ) and a relation called incidence. If we say that the point and the line are incident. +

  • The dual of an incidence structure is the structure given by

    Where .

  • The Incidence graph also called the Levi Graph of an incidence structure is the graph where

    • The incidence graph is bipartite.
    • Any bipartite graph can define an incidence structure by declaring one partition as points and the other as edges.
    • A bipartite graph contains both an incidence structure and its dual.
  • A partial linear space is an incidence structure where any two points are incident with at most one line.

    • Two points are collinear if they are joined by a line (they are both incident to the line).
    • Two lines are concurrent if they meet at a point (they are both incident to the point).
  • (Godsil 5.1.1) The incidence graph of a partial linear space has girth at least .

  • An automorphism of an incidence structure is a permutation of such that

    • An incidence preserving of such that and is called a duality.
    • An incidence structure with a duality is self-dual. Such a structure is isomorphic to its dual.

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