-
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.
- An incidence preserving