On graphs whose local subgraphs are strongly regular with parameters (144, 39, 6, 12)

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Обратные задачи в теории графов: графы без треугольников

Graph r for a distance-regular graph r of diameter 3 can be strongly regular for i 2 or i = 3. Finding intersection array of graph r by t lio parameters of ri 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 it is consider the case when graph r3 is strongly regular without triangles and v < 100000. © 2021 Махнев А.А., Белоусов И.Н., Падучих Д.В. All Rights Reserved.Работа выполнена при финансовой поддержке РФФИ и ГФЕН Китая в рамках научного проекта № 20-51-53013

On graphs in which neighborhoods of vertices are isomorphic to the Higman-Sims graph

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 F-graphs, where F is the class of strongly regular graphs without triangles. © 2012 Pleiades Publishing, Ltd