On strongly regular extensions of generalized quadrangles
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 497-505

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The parameters $s$, $t$ of a generalized quadrangle are said to be classical if $s=p^\alpha$ and $t=p^\beta$ for some prime number $p$ and nonnegative integers $\alpha$ and $\beta$. A escription is obtained for the possible parameters of strongly regular graphs in which the neighborhoods of the vertices are generalized quadrangles with quasiclassical parameters.
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     author = {A. A. Makhnev},
     title = {On strongly regular extensions of generalized quadrangles},
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A. A. Makhnev. On strongly regular extensions of generalized quadrangles. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 497-505. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a11/