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This article is cited in 1 scientific paper (total in 1 paper)
Discrete mathematics and mathematical cybernetics
Inverse problems of graph theory: generalized quadrangles
A. A. Makhnevab, M. S. Nirovac a N.N. Krasovsky Institute of Mathematics and Meckhanics,
str. S. Kovalevskoy, 16,
620990, Ekaterinburg, Russia
b Ural Federal University
c Kabardino-Balkarian State University named after H.M. Berbekov,
st. Chernyshevsky, 175,
360004, Nalchik, Russia
Abstract:
Graph $\Gamma_i$ for a distance-regular graph $\Gamma$ of diameter 3 can be strongly regular for $i=2$ or $i=3$. Finding parameters of $\Gamma_i$ by the intersection array of graph $\Gamma$ is a direct problem. Finding intersection array of graph $\Gamma$ by the parameters of $\Gamma_i$ is an inverse problem. Earlier direct and inverse problems have been solved by A.A. Makhnev, M.S. Nirova for $i=3$ and by A.A. Makhnev and D.V. Paduchikh for $i=2$.
In this work the inverse problem has been solved in cases when graphs $\Gamma_2$, $\Gamma_3$, $\bar \Gamma_2$ or $\bar \Gamma_3$ are pseudo-geometric for generalized quadrangle. In particular, graphs $\Gamma_2$ and $\bar \Gamma_3$ are not to be a pseudo-geometric for generalized quadrangle.
Keywords:
distance regular graph, graph $\Gamma$ with strongly regular graph $\Gamma_i$.
Received May 20, 2018, published August 22, 2018
Citation:
A. A. Makhnev, M. S. Nirova, “Inverse problems of graph theory: generalized quadrangles”, Sib. Èlektron. Mat. Izv., 15 (2018), 927–934
Linking options:
https://www.mathnet.ru/eng/semr966 https://www.mathnet.ru/eng/semr/v15/p927
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