×

On regular Terwilliger graphs with \(\mu=2\). (English. Russian original) Zbl 0874.05062

Sib. Math. J. 37, No. 5, 997-999 (1996); translation from Sib. Mat. Zh. 37, No. 5, 1132-1134 (1996).
The monograph [A. E. Brouwer, A. M. Cohen and 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.

MSC:

05E30 Association schemes, strongly regular graphs

Citations:

Zbl 0747.05073
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Berlin etc. (1989). · Zbl 0747.05073
[2] J. I. Hall, ”Locally Petersen graphs,” J. Graph Theory Ser. A,4, No. 2, 173–187 (1980). · Zbl 0427.05038 · doi:10.1002/jgt.3190040206
[3] P. Terwilliger, ”Distance-regular graphs with girth 3 or 4. I,” J. Combin. Theory Ser. B,39, No. 3, 265–281 (1985). · Zbl 0588.05039 · doi:10.1016/0095-8956(85)90054-1
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.