Parallelogram-free distance-regular graphs having completely regular strongly regular subgraphs
Hiroshi Suzuki
DOI: 10.1007/s10801-009-0167-2
Abstract
Let Γ =( X, R) be a distance-regular graph of diameter d. A parallelogram of length i is a 4-tuple xyzw consisting of vertices of Γ such that
tial ( x, y)=
tial ( z, w)=1,
tial ( x, z)= i, and
tial ( x, w)=
tial ( y, w)=
tial ( y, z)= i - 1. A subset Y of X is said to be a completely regular code if the numbers
tial ( x, y)=
tial ( z, w)=1,
tial ( x, z)= i, and
tial ( x, w)=
tial ( y, w)=
tial ( y, z)= i - 1. A subset Y of X is said to be a completely regular code if the numbers
| p i, j= | G j( x) Ç Y | ( i, j Ĩ {0,1, \frac{1}{4} , d}) \pi_{i,j}=|\Gamma_{j}(x)\cap Y|\quad (i,j\in \{0,1,\ldots,d\})
Pages: 401–413 Keywords: keywords distance-regular graph; association scheme; homogeneity; completely regular code Full Text: PDF References1. Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance-Regular Graphs. Springer, Berlin (1989)
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