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Distance-Regular Graphs
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In this paper, a connected simple graph with vertex set X of diameter d is considered, and the authors define Ri X2 by (x, y) Ri whenever x and y have graph distance.Abstract:
Consider a connected simple graph with vertex set X of diameter d. Define Ri X2 by (x, y) Ri whenever x and y have graph distanceread more
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The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters
TL;DR: The smallest eigenvalue and the second largest eigen value in absolute value of the graphs of the relations of classical $P$- and $Q$-polynomial association schemes are studied.
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Eigenvalue interlacing and weight parameters of graphs
TL;DR: This work shows how to use interlacing for proving results about some weight parameters and pseudo-regular partitions of a graph.
Journal ArticleDOI
The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme
TL;DR: It is proved that any irreducible T-module W is both thin and dual thin in the sense of Terwilliger, and the isomorphism class of W as a T- module is determined by two parameters, the dual endpoint and diameter of W.
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Codes from incidence matrices and line graphs of Hamming graphs
TL;DR: It is shown that the codes from the incidence matrices of H(n,m) can be used for full permutation decoding for all m,n>=3.
Posted Content
Shilla distance-regular graphs
Jack H. Koolen,Jongyook Park +1 more
TL;DR: In this paper, it was shown that there are finitely many Shilla distance-regular graphs G with fixed b(G)>=2 and fixed b=b(G):=k/a3.
References
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Journal ArticleDOI
Equilateral point sets in elliptic geometry
J.H. van Lint,J.J. Seidel +1 more
TL;DR: In this paper, the authors highlight equilateral point sets in elliptic geometry and show that Paley's construction may be reversed to obtain a C -matrix of order 46, in view of the existence of a Hadamard matrix of order 92.
BookDOI
On construction and identification of graphs
TL;DR: The problem of graph identification has been studied in the theory of permutation groups for a long time, see as mentioned in this paper for a discussion of the main points of the problem and an algorithm for graph identification.