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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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Linear programming bounds for regular graphs
TL;DR: In this article, the authors used the linear programming method to obtain bounds for the number of vertices of connected regular graphs endowed with given distinct eigenvalues, motivated from the theory of association scheme.
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An Erdős-Ko-Rado theorem for finite classical polar spaces
TL;DR: In this paper, it was proved that the set consisting of all subspaces of rank n that contain a given point is a largest Erdős-Ko-Rado set.
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Bounds on special subsets in graphs, eigenvalues and association schemes
TL;DR: In this paper, the Laplace spectrum of a graph has been used to obtain bounds on the number of vertices that are not adjacent to a given vertex and that have µ common neighbours with that vertex.
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Energy bounds for codes in polynomial metric spaces
Peter Boyvalenkov,Peter Boyvalenkov,Peter D Dragnev,Douglas P. Hardin,Edward B. Saff,Maya Stoyanova +5 more
TL;DR: In this article, a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces) was presented, where lower bounds via the linear programming techniques of Delsarte and Levenshtein are universally optimal in the sense that they apply to a broad class of energy functionals and cannot be improved for the specific subspace.
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Eigenvalues of association schemes of quadratic forms
TL;DR: In this paper, eigenvalues of Qua(n,q) are computed, where q is a power of 2, and as an application, two fusion schemes of QuA(n),q are discussed and their dual schemes are constructed.
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.