A partial geometry incidence structure of points
and lines such that every line contains
The point graph of a partial geometry, obtained by joining two points when they are on a common line ,
is a strongly regular graph with parameters
The lines of the partial geometry give the Delsarte cliques that make the point graph a geometric
graph . A strongly regular graph with
these parameters is called a pseudogeometric
graph for point
graph of an actual partial geometry.
For example, the nonexistent McLaughlin geometry would be a partial geometry point graph
would have parameters
See also Block Design ,
Generalized Quadrangle ,
Geometric Graph ,
McLaughlin
Geometry ,
Point Graph ,
Pseudogeometric
Graph ,
Strongly Regular Graph
Explore with Wolfram|Alpha
References Bose, R. "Strongly Regular Graphs, Partial Geometries and Partially Balanced Designs." Pacific J. Math. 13 , 389-419,
1963. Brouwer, A. E. and van Lint, J. H. "Strongly Regular
Graphs and Partial Geometries." In Enumeration
and Design: Papers from the Conference on Combinatorics Held at the University of
Waterloo, Waterloo, Ont., June 14-July 2, 1982 Thas, J. A. "Combinatorics of Partial Geometries and
Generalized Quadrangles." In Higher
Combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976).
Cite this as:
Weisstein, Eric W. "Partial Geometry."
From MathWorld https://mathworld.wolfram.com/PartialGeometry.html
Subject classifications
is an incidence structure of points
and lines such that every line contains 
points, every point lies on 
lines, any two points lie on at most one line, and, for
a point 
not on a line 
,
there are exactly 
lines through 
that meet 
.
even when it is not known to be, or is not, the point
graph of an actual partial geometry.
, whose point graph
would have parameters 
.
