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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1506–1512 (Mi semr1030)  

Discrete mathematics and mathematical cybernetics

Distance-regular graphs with intersectuion arrays $\{42,30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist

I. N. Belousova, A. A. Makhnevba

a N.N. Krasovskii Institute of Mathematics and Mechanics, 16, S.Kovalevskaya st., Yekaterinburg, 620990, Russia
b Vyatskii Gosudarstvennyi Universitet

Abstract: Koolen and Park obtained the list of intersection arrays for Shilla graphs with $b=3$. In particular distance-regular graph with intersectuion array $\{42,30,12;1,6,28\}$ is Shilla graphs with $b=3$. Gavrilyuk and Makhnev investigated properties of a graph with intersectuion array $\{60,45,8;1,12,50\}$. We proved that distance-regular graphs with intersectuion arrays $\{42, 30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist.

Keywords: distance-regular graph, Shilla graph, triple intersection numbers.

DOI: https://doi.org/10.33048/semi.2018.15.125

Full text: PDF file (144 kB)
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Bibliographic databases:

Document Type: Article
UDC: 519.17
MSC: 05C25
Received October 10, 2018, published November 26, 2018

Citation: I. N. Belousov, A. A. Makhnev, “Distance-regular graphs with intersectuion arrays $\{42,30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist”, Sib. Èlektron. Mat. Izv., 15 (2018), 1506–1512

Citation in format AMSBIB
\Bibitem{BelMak18}
\by I.~N.~Belousov, A.~A.~Makhnev
\paper Distance-regular graphs with intersectuion arrays $\{42,30,12;1,6,28\}$ and $\{60,45,8;1,12,50\}$ do not exist
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1506--1512
\mathnet{http://mi.mathnet.ru/semr1030}
\crossref{https://doi.org/10.33048/semi.2018.15.125}


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