On regular Terwilliger graphs with \(\mu=2\)
The monograph [\textit{A. E. Brouwer}, \textit{A. M. Cohen} and \textit{A. Neumaier}, Distance-regular graphs, Springer, Berlin (1989; Zbl 0747.05073)] put the following problem: Is it true that a connected regular Terwilliger graph is either the \(\mu\)-extension of some graph or the subgraph \([a]- K(a)\) is regular for every vertex \(a\) of the graph? (We note that \([a]\) is the neighbourhood of \(a\), and \(K(a)\) is a core of \(a\).) The author solves this problem for \(\mu=2\). More precisely, he proves that a connected regular Terwilliger graph with \(\mu=2\) is either the 2-extension of a graph with \(\mu=1\) or a locally \(\lambda\) graph.
scientific article; zbMATH DE number 1023912