Delsarte Set Graphs with Small c(2)

Title
Delsarte Set Graphs with Small c(2)
Author(s)
방세정J.Koolen[J.Koolen]A.Hiraki[A.Hiraki]
Issue Date
201003
Publisher
SPRINGER TOKYO
Citation
GRAPHS AND COMBINATORICS, v.26, no.2, pp.147 - 162
Abstract
Let Gamma be a Delsarte set graph with an intersection number c(2) (i.e., a distance-regular graph with a set C of Delsarte cliques such that each edge lies in a positive constant number n(C) of Delsarte cliques in C). We showed in Bang et al. (J Combin 28:501-506, 2007) that if psi(1) > 1 then c(2) >= 2 psi(1) where psi(1) := vertical bar Gamma(1)(x)boolean AND C vertical bar for x is an element of V(Gamma) and C aDelsarte clique satisfying d(x, C) = 1. In this paper, we classify Gamma with the case c(2) = 2 psi(1) > 2. As a consequence of this result, we show that if c(2) <= 5 and psi(1) > 1 then Gamma is either a Johnson graph or a folded Johnson graph (J) over bar (4s, 2s) with s >= 3.
URI
http://hdl.handle.net/YU.REPOSITORY/22753http://dx.doi.org/10.1007/s00373-010-0905-1
ISSN
0911-0119
Appears in Collections:
이과대학 > 수학과 > Articles
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