Berlekamp–Van Lint–Seidel graph

This means that it has 243 vertices, 22 edges per vertex (for a total of 2673 edges), exactly one shared neighbor per pair of adjacent vertices, and exactly two shared neighbors per pair of non-adjacent vertices.

It was constructed by Elwyn Berlekamp, J. H. van Lint, and Johan Jacob Seidel [de] as the coset graph of the ternary Golay code.

[2] It is also an integral graph, meaning that the eigenvalues of its adjacency matrix are integers.

[4] 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.

[5] Conway's 99-graph problem concerns the existence of another of these graphs, the one with parameters