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Diskr. Mat., 2020, Volume 32, Issue 1, Pages 74–80 (Mi dm1595)  

On a distance-regular graphs with $c_2=2$

A. A. Makhnevab, M. S. Nirovaab

a Institute of Mathematics and Mechanics UB RAS
b Kabardino-Balkarskii State University

Abstract: Let $\Gamma$ be a distance-regular graph of diameter $d=3$ with $c_2=2$. Then local subgraph $\Delta$ of the vertex $w$ of $\Gamma$ is a partial line spase. By some Brouwer-Neumaier result either $\Delta$ is the union of $(a_1+1)$-cliques or $k\ge a_1(a_1+3)/2$, and in the case equality we have $k=5, \lambda=2$ and $\Gamma$ is icosahedron.
A.A. Makhnev, M.P. Golubyatnikov and Wenbin Guo investigate distance-regular graphs $\Gamma$ with $\Gamma_3$ being pseudo-geometric graph for net. They found a new infinite series $\{2u^2-2m^2+4m-3,2u^2-2m^2,u^2-m^2+4m-2;1,2,u^2-m^2\}$ feasible intersection arrays for such graphs with $c_2=2$. In the paper it is proved that some graphs with arrays from this series do not exist. Also it is proved that distance-regular graph with intersection array $\{22,16,5;1,2,20\}$ does not exist.

Keywords: distance-regular graph, partial line space, graph with $c_2=2$.

Funding Agency Grant Number
Ural Branch of the Russian Academy of Sciences 18-1-1-17
Ministry of Education and Science of the Russian Federation 02.A03.21.0006


DOI: https://doi.org/10.4213/dm1595

Full text: PDF file (435 kB)
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Bibliographic databases:

UDC: 519.172
Received: 24.10.2019

Citation: A. A. Makhnev, M. S. Nirova, “On a distance-regular graphs with $c_2=2$”, Diskr. Mat., 32:1 (2020), 74–80

Citation in format AMSBIB
\Bibitem{MakNir20}
\by A.~A.~Makhnev, M.~S.~Nirova
\paper On a distance-regular graphs with $c_2=2$
\jour Diskr. Mat.
\yr 2020
\vol 32
\issue 1
\pages 74--80
\mathnet{http://mi.mathnet.ru/dm1595}
\crossref{https://doi.org/10.4213/dm1595}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4075903}


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