Izv. Vyssh. Uchebn. Zaved. Mat., 2022 Number 9, Pages 64–69
(Mi ivm9812)
The Koolen-Park bound and distance-regular graphs without $m$ -clavs A. A. Makhnev ab ,
Wenbin Guo ac ,
K. S. Efimov deb a School of Science, Hainan University, Haikou, Hainan, 570228, P.R. China b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskoy str., Yekaterinburg, 620137 Russia c University of Science and Technology of China, Hefei, 230026, P. R. China d Ural State Mining University, 30 Kuibysheva str., Yekaterinburg, 620144 Russia e Ural Federal University, 19 Mira str., Yekaterinburg, 620002 Russia Abstract:
Using the Koolen-Park bound, we prove that distance-regular graphs with intersection arrays
$\{83,54,21;1,6,63\}$ ,
$\{80,54,12;1,6,60\}$ and
$\{93,64,24;1,12,62\}$ do not exist.
Keywords:
distance-regular graph, Koolen-Pack boundary, $m$ -clav.
UDC:
519.17 Received: 29.11.2021
Revised: 29.11.2021
Accepted: 29.06.2022
DOI:
10.26907/0021-3446-2022-9-64-69
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