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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 3, Pages 187–194 (Mi timm852)  

On strongly regular graphs with $b_1<24$

M. S. Nirova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Let $\Gamma$ be a connected edge-regular graph with parameters $(v,k,\lambda)$, and let $b_1=k-\lambda-1$. It is well-known that, if $b_1=1$, then $\Gamma$ is either a polygon or a complete multipartite graph with parts of order 2. Graphs with $b_1\le4$ were classified earlier. The investigation of graphs even in the case $b_1=5$ involves great difficulties. However, for strongly regular graphs, the situation is much simpler. In this paper, we classify strongly regular graphs with $b_1<24$.

Keywords: strongly regular graph, partial geometry, pseudo geometric graph.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 283, suppl. 1, 111–118

Bibliographic databases:

UDC: 519.17
Received: 10.12.2011

Citation: M. S. Nirova, “On strongly regular graphs with $b_1<24$”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 187–194; Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 111–118

Citation in format AMSBIB
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\by M.~S.~Nirova
\paper On strongly regular graphs with $b_1<24$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 3
\pages 187--194
\mathnet{http://mi.mathnet.ru/timm852}
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 283
\issue , suppl. 1
\pages 111--118
\crossref{https://doi.org/10.1134/S0081543813090113}
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