On graphs in which neighborhoods of vertices are isomorphic to the Higman--Sims graph
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 189-198
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The Higman–Sims graph is the unique strongly regular graph with parameters $(100,22,0,6)$. In this paper, amply regular graphs in which neighborhoods of vertices are isomorphic to the Higman–Sims graph are classified. This result continues the investigation of amply regular locally $\mathcal F$-graphs, where $\mathcal F$ is the class of strongly regular graphs without triangles.
Keywords:
strongly regular graph, Higman–Sims graph, locally $\mathcal F$-graph.
@article{TIMM_2011_17_4_a19,
author = {A. A. Makhnev and D. V. Paduchikh},
title = {On graphs in which neighborhoods of vertices are isomorphic to the {Higman--Sims} graph},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {189--198},
publisher = {mathdoc},
volume = {17},
number = {4},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a19/}
}
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%0 Journal Article %A A. A. Makhnev %A D. V. Paduchikh %T On graphs in which neighborhoods of vertices are isomorphic to the Higman--Sims graph %J Trudy Instituta matematiki i mehaniki %D 2011 %P 189-198 %V 17 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a19/ %G ru %F TIMM_2011_17_4_a19
A. A. Makhnev; D. V. Paduchikh. On graphs in which neighborhoods of vertices are isomorphic to the Higman--Sims graph. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 189-198. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a19/