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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

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

This article is cited in 8 papers

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.

UDC: 519.17

MSC: 05C25

Received October 10, 2018, published November 26, 2018

DOI: 10.33048/semi.2018.15.125



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