Graphs with the n-e.c. adjacency property constructed from affine planes Original Research Article

We give new examples of graphs with the n-e.c. adjacency property. Few explicit families of n-e.c. graphs are known, despite the fact that almost all finite graphs are n-e.c. Our examples are collinearity graphs of certain partial planes derived from affine planes of even order. We use probabilistic and geometric techniques to construct new examples of n-e.c. graphs from partial planes for all n, and we use geometric techniques to give infinitely many new explicit examples if image. We give a new construction, using switching, of an exponential number of non-isomorphic n-e.c. graphs for certain orders.