Geodesic
Exceptional pseudogeometric graphs with eigenvalue r
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 68-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. Neumaier enumerated the parameters of strongly regular graphs with smallest eigenvalue $-m$. As a corollary it is proved that for a positive integer $r$ there exist only finitely many pseudogeometric graphs for $pG_{s-r}(s,t)$ with parameters different from the parameters of the net $pG_{s-r}(s,s-r)$ and from the parameters of the $pG_{s-r}(s,(s-r)(r+1)/r)$ graph complementary to the line graph of a Steiner 2-design ($s$ is a multiple of $r$). In this paper we explicitly specify functions $f(r)$ and $g(r)$ such that for $s>f(r)$ or $t>g(r)$ any pseudogeometric graph for $pG_{s-r}(s,t)$ has parameters of the net $pG_{s-r}(s,s-r)$ or parameters of $pG_{s-r}(s,(s-r)(r+1)/r)$.
Keywords: strongly regular graph, pseudogeometric graph. 
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     title = {Exceptional pseudogeometric graphs with eigenvalue r},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a7/}
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A. Kh. Zhurtov. Exceptional pseudogeometric graphs with eigenvalue r. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 68-72. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a7/

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