For a distance-regular graph (Formula presented.) of diameter 3, the graph (Formula presented.) can be strongly regular only if either i=2 or i=3. For the case inwhich (Formula presented.) is strongly regular, Koolen and his coauthors foundparameters of (Formula presented.) in terms of the intersection array of (Formula presented.) (these parameters were obtained independently byMakhnev and Paduchikh). In this case, one of the eigenvalues of (Formula presented.) is (Formula presented.). In the present article, we consider graphs with eigenvalues (Formula presented.) and (Formula presented.). We prove that the intersection array of (Formula presented.) is (Formula presented.). For (Formula presented.), we show that the intersection array of (Formula presented.) is either (Formula presented.), or (Formula presented.), or (Formula presented.), or (Formula presented.). © 2023, Pleiades Publishing, Ltd.