A pseudogeometric graph for strongly
regular graph with the same parameters as the point
graph of a partial geometry
The term does not assert that the graph is the point graph of an actual partial geometry . When
such a graph is realized by a partial geometry ,
the lines of the geometry give the Delsarte
cliques that make the graph a geometric graph .
For example, the McLaughlin graph is a pseudogeometric graph for McLaughlin
geometry does not exist.
See also Geometric Graph ,
McLaughlin Geometry ,
McLaughlin Graph ,
Partial
Geometry ,
Point Graph ,
Strongly
Regular Graph
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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 Östergård, P. R. J. and Soicher, L. H.
"There is No McLaughlin Geometry." 12 Jul 2016. https://arxiv.org/abs/1607.03372 .
Cite this as:
Weisstein, Eric W. "Pseudogeometric Graph."
From MathWorld https://mathworld.wolfram.com/PseudogeometricGraph.html
Subject classifications
is a strongly
regular graph with the same parameters as the point
graph of a partial geometry 
, namely
,
but Östergård and Soicher (2016) proved that the corresponding McLaughlin
geometry does not exist.
