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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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Commutative association schemes
William J. Martin,Hajime Tanaka +1 more
TL;DR: The goal of the present survey is to discuss the most important new developments in several directions, including Gelfand pairs, cometric association schemes, Delsarte Theory, spin models and the semidefinite programming technique.
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The Gewirtz Graph
TL;DR: In this article, it was shown that the Coxeter graph and Sylvester graph are induced subgraphs, and that the Sylvesters and Coxeter graphs can be viewed as a set of connected sub-graphs.
Journal ArticleDOI
Permutation group approach to association schemes
TL;DR: Several applications of schemes to constructing polynomial-time algorithms, in particular, graph isomorphism tests, are discussed.
Posted Content
Leonard pairs from 24 points of view
TL;DR: In this paper, the authors consider a pair of linear transformations that satisfy both conditions below: (i) there exists a basis for $V$ with respect to which the matrix representing $A$ is diagonal and the matrix represented $A^*$ is irreducible tridiagonal.
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Berry Esseen Bounds for Combinatorial Central Limit Theorems and Pattern Occurrences, using Zero and Size Biasing
TL;DR: The zero-and size-bias bounds for random permutations are derived in this article for combinatorial central limit theorems in which the random permutation has either the uniform distribution or one that is constant over permutations with the same cycle type, with no fixed points.
References
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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.