Distance-regular Terwilliger graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1075-1082
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Let $\Gamma$ be a distance-regular graph and its local subgraphs are isomorphic the Hoffman-Singleton graph. A.L. Gavrilyuk and A.A. Makhnev proved that $\Gamma$ is the Terwilliger graph with intersection array $\{50,42,9;1,2,42\}$ or $\{50,42,1;1,2,50\}$. In this paper we prove that Terwilliger graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist.
Keywords:
distance-regular graph, Terwilliger graph, triple intersection numbers.
@article{SEMR_2021_18_2_a39,
author = {A. A. Makhnev and M. S. Nirova},
title = {Distance-regular {Terwilliger} graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {1075--1082},
publisher = {mathdoc},
volume = {18},
number = {2},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a39/}
}
TY - JOUR
AU - A. A. Makhnev
AU - M. S. Nirova
TI - Distance-regular Terwilliger graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist
JO - Sibirskie èlektronnye matematičeskie izvestiâ
PY - 2021
SP - 1075
EP - 1082
VL - 18
IS - 2
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a39/
LA - ru
ID - SEMR_2021_18_2_a39
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%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2021
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%I mathdoc
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%F SEMR_2021_18_2_a39
A. A. Makhnev; M. S. Nirova. Distance-regular Terwilliger graphs with intersection arrays $\{50,42,1;1,2,50\}$ and $\{50,42,9;1,2,42\}$ do not exist. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1075-1082. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a39/