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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
Citations
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Journal ArticleDOI
Width and dual width of subsets in polynomial association schemes
TL;DR: It is shown that any subset of minimal width is a completely regular code and that any subsection of minimal dual width induces a cometric association scheme in the original.
Journal ArticleDOI
Problems in Algebraic Combinatorics
TL;DR: This is a list of open problems, mainly in graph theory and all with an algebraic flavour, except for 6.1 and 12.2, which are either folklore, or are stolen from other people.
Expanding and forwarding
TL;DR: In this article, a connection between the forwarding indices and algebraic parameters like the smallest eigenvalue of the Laplacian or the genus of the graph is made, showing that certain graphs have eccentricity close to the diameter.
Journal ArticleDOI
Shilla distance-regular graphs
Jack H. Koolen,Jongyook Park +1 more
TL;DR: It is shown that there are finitely many Shilla distance-regular graphs @C with fixed b(@C)>=2 and b( @C)=3, and a new existence condition for distance- regular graphs, in general is given.
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On upper bounds for code distance and covering radius of designs in polynomial metric spaces
Gábor Fazekas,V.I. Levenshtein +1 more
TL;DR: New upper bounds for code distance and covering radius of designs in arbitrary polynomial metric spaces are presented and it is proved that this bound is attained for all tight 2k-design.
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.