On extensions of small strongly regular graphs with eigenvalue 3

Abstract

Previously, the authors found the parameters of exceptional strongly regular graphs with eigenvalue 3 (theorem). It is proved that, if Γ is a distance-regular graph whose local subgraphs are strongly regular with parameters listed in items (3)–(10) of the theorem, then Γ is a strongly regular graph, Taylor graph, or a graph with intersection array {100, 66, 1; 1, 33, 100}.