In graph theory, the Berlekamp–Van Lint–Seidel graph is a locally linear strongly regular graph with parameters
(243,22,1,2)
This graph is the Cayley graph of an abelian group. Among abelian Cayley graphs that are strongly regular and have the last two parameters differing by one, it is the only graph that is not a Paley graph. It is also an integral graph, meaning that the eigenvalues of its adjacency matrix are integers. Like the
9 x 9
There are five possible combinations of parameters for strongly regular graphs that have one shared neighbor per pair of adjacent vertices and exactly two shared neighbors per pair of non-adjacent vertices. Of these, two are known to exist: the Berlekamp–Van Lint–Seidel graph and the 9-vertex Paley graph with parameters
(9,4,1,2)
(99,14,1,2)