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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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Pseudo-distance-regularized graphs are distance-regular or distance-biregular
TL;DR: In this paper, the authors prove that a pseudo-distance-regular graph around each of its vertices is either distance-regular or distance-biregular, by using a combinatorial approach.
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Uniqueness of certain association schemes
TL;DR: The uniqueness of the two association schemes which appear in recent work of Henry Cohn and others in connection with their study of universally optimal spherical codes in Euclidean spaces is proved.
Journal ArticleDOI
Distance-Regular Shilla Graphs with b2 = c2
TL;DR: In this paper, it was proved that a Shilla graph with b2 = c2 and noninteger eigenvalues has the following intersection array: $$\left\{ {\frac{{{b^2}\left( {b - 1} \right)}}{2,
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Q-polynomial distance-regular graphs and a double affine Hecke algebra of rank one
TL;DR: In this article, the authors studied the relationship between Q -polynomial distance-regular graphs and the double affine Hecke algebra of type (C 1 ∨, C 1 ).
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.