  A result of Erd\"os and R\'enyi shows that for a fixed integer n almost all
graphs satisfy the n-e.c. adjacency property. However, there are few explicit
constructions of n e.c. graphs for n > 2, and almost all known families of
n-e.c. graphs are strongly regular graphs. In this paper we derive parameter
bounds on strongly regular n-e.c. graphs constructed from the point sets of
partial geometries. This work generalizes bounds on n-e.c. block intersection
graphs of balanced incomplete block designs given by McKay and Pike. It also
relates to work by Griggs, Grannel, and Forbes' determining 3-e.c. graphs that
are block intersection graphs of Steiner triple systems. In addition to these
bounds, we give examples of strongly regular graphs that contain every possible
subgraph of small order but are not n-e.c. for n > 2.
