Journal ArticleDOI
Symmetric Conference Matrices of Order pq 2 + 1
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A conference matrix of order n is a square matrix C with zeros on the diagonal and ± 1 elsewhere, which satisfies the orthogonality condition CCT = (n − 1)I as mentioned in this paper.Abstract:
A conference matrix of order n is a square matrix C with zeros on the diagonal and ±1 elsewhere, which satisfies the orthogonality condition CCT = (n — 1)I. If in addition C is symmetric, C = CT, then its order n is congruent to 2 modulo 4 (see [5]). Symmetric conference matrices (C) are related to several important combinatorial configurations such as regular two-graphs, equiangular lines, Hadamard matrices and balanced incomplete block designs [1; 5; and 7, pp. 293-400]. We shall require several definitions.read more
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BookDOI
Spectra of graphs
TL;DR: This book gives an elementary treatment of the basic material about graph Spectra, both for ordinary, and Laplace and Seidel spectra, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.
Book
Distance-Regular Graphs
TL;DR: 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.
Hadamard matrices, Sequences, and Block Designs
Jennifer Seberry,Mieko Yamada +1 more
TL;DR: Seberry and Yamada as discussed by the authors considered the problem of finding the maximal determinant of real matrices with entries on the unit disc, and showed that Hadamard matrices satisfy the equality of the following inequality.
Dissertation
On orthogonal matrices
TL;DR: In this paper, Behbahani et al. showed that the OD(l2; 1,1, 1, 9) is the only orthogonal design constructible from 16 circulant matrices, whenever n > 1 is an odd integer, and showed that for each integer n for which 4n is the order of a Hadamard matrix and 8n 2 + 1 is a prime, there is a productive regular matrix of order 16n 2 (8n 2 ) 2.
Book ChapterDOI
Two-graphs, a second survey
J.J. Seidel,D.E. Taylor +1 more
TL;DR: A two-graph is a vertex set Ω and a collection Δ of 3-subsets of Ω such that every 4-subset of a given vertex set contains an even number of 3subsets from Δ as discussed by the authors.
References
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Book ChapterDOI
A survey of two-graphs
TL;DR: In this article, a one-to-one correspondence between the two-graphs and the switching classes of graphs on the set of n elements is established, and the correspondence is shown to hold also for the binary maps with vanishing co-boundaries.
Journal ArticleDOI
Orthogonal matrices with zero diagonal
J.M. Goethals,J.J. Seidel +1 more
TL;DR: In this article, the negacyclic C-matrices of order v = 0 (mod 4) were shown to have no multipliers, unless v = 1 + pk, p prime.