A. A. Makhnev, D. V. Paduchikh, “On graphs in which neighborhoods of vertices are isomorphic to the Higman–Sims graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 4,Pages <nobr>189

This article is cited in 2 papers

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

A. A. Makhnev^ab, D. V. Paduchikh^a

^a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^b Ural Federal University

Abstract: 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.

UDC: 519.17

Received: 28.01.2011