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Distance-regular graph with intersection array $\{27, 20, 7; 1, 4, 21\}$ does not exist
Konstantin S. Efimovab, Alexander A. Makhnevcb a Ural State University of Economics, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
c Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Аннотация:
In the class of distance-regular graphs of diameter $3$ there are $5$ intersection arrays of graphs with at most $28$ vertices and noninteger eigenvalue. These arrays are $\{18, 14, 5; 1, 2, 144\}$, $\{18, 15, 9; 1, 1, 10\}$, $\{21, 16, 10; 1, 2, 12\}$, $\{24, 21, 3; 1, 3, 18\}$, and $\{27, 20, 7; 1, 4, 21\}$. Automorphisms of graphs with intersection arrays $\{18, 15, 9; 1, 1, 10\}$ and $\{24, 21, 3; 1, 3, 18\}$ were found earlier by A. A. Makhnev and D. V. Paduchikh. In this paper, it is proved that a graph with the intersection array $\{27, 20, 7; 1, 4, 21\}$ does not exist.
Ключевые слова:
distance-regular graph, graph $\Gamma$, with strongly regular graph $\Gamma_3$, automorphism.
Образец цитирования:
Konstantin S. Efimov, Alexander A. Makhnev, “Distance-regular graph with intersection array $\{27, 20, 7; 1, 4, 21\}$ does not exist”, Ural Math. J., 6:2 (2020), 63–67
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj126 https://www.mathnet.ru/rus/umj/v6/i2/p63
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