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2009

Shilla distance-regular graphs

Koolen, Jack H., Park, Jongyook

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Understand

A Shilla distance-regular graph G (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3.

We will show that a3 divides k for a Shilla distance-regular graph G, and for G we define b=b(G):=k/a3.
In this paper we will show that there are finitely many Shilla distance-regular graphs G with fixed b(G)>=2.
Also, we will classify Shilla distance-regular graphs with b(G)=2 and b(G)=3.

Shilla distance-regular graphs · Around

Built on

A.E. Brouwer, A.M. Cohen and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, 1989
1989
Earlier work this paper cites.
W.H. Haemers, Interlacing eigenvalues and graphs, Linear Algebra Appl. 226/228 (1995), 593-616
1995
Earlier work this paper cites.

Similar

A. Juri s ˇ \check{{\rm s}} i c ´ \acute{{\rm c}} and J. Koolen, Nonexistence of some antipodal distance-regular graphs of diameter four, European J. Combin. 21 (2000), 1039-1046
2000
Cited alongside, same era.

Then

K. Coolsaet, A distance-regular graph with intersection array {21, 16, 8; 1, 4, 14} does not exist, European J. Combin. 26 (2005), 709-716
2005
Later among the works it cites.

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