Abstract
In this chapter we return to the theme of combinatorial regularity with the study of strongly regular graphs. In addition to being regular, a strongly regular graph has the property that the number of common neighbours of two distinct vertices depends only on whether they are adjacent or nonadjacent. A connected strongly regular graph with connected complement is just a distance-regular graph of diameter two. Any vertex-transitive graph with a rank-three automorphism group is strongly regular, and we have already met several such graphs, including the Petersen graph, the Hoffman-Singleton graph, and the symplectic graphs of Section 8.11.
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