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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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Bounds for codes and designs in complex subspaces
TL;DR: Using Delsarte’s linear programming techniques, the bounds for real subspaces recently found by Bachoc, Bannai, Coulangeon and Nebe are found and the bounds generalize those ofDelsarte, Goethals and Seidel for codes and designs on the complex unit sphere.
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Combinatorial designs with two singular values I: uniform multiplicative designs
E.R. van Dam,Edward Spence +1 more
TL;DR: In this paper, the authors studied combinatorial designs whose incidence matrix has two distinct singular values and classified all such designs with smallest singular value at most √2, generalize the Bruck-Ryser-Chowla conditions, and enumerate, partly by computer, all uniform multiplicative designs on at most 30 points.
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Tight Graphs and Their Primitive Idempotents
TL;DR: In this paper, the authors prove the following two theorems: (1) The entry-wise product E F is a scalar multiple of a primitive idempotent of a distance-regular graph with diameter d ≥ 3, and (2) Theorem 1.
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Association schemes generated by a non-symmetric relation of valency 2
M. Hirasaka,Mikhail Muzychuk +1 more
TL;DR: Some observations on association schemes with a relation of valency 2 from the representation theory of Bose-Mesner algebras and the basic structure theory are given and Li's conjecture that any finite simple group is a connected 2-DCI-group is proved.
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On the spectrum of Wenger graphs
TL;DR: All distinct eigenvalues of the adjacency matrix of W m ( q ) and their multiplicities are determined and the results on Wenger graphs are surveyed.
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.