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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
On Modular Standard Modules of Association Schemes
TL;DR: In this article, the structure of the modular standard modules of association schemes of class two was determined and the theoretical interpretation for the p-rank theory for strongly regular graphs was given.
Journal ArticleDOI
Antipodal Distance-transitive Covers of Complete Bipartite Graphs
TL;DR: This paper completes the classification of antipodal distance-transitive covers of the complete bipartite graphs Kk,k, wherek?3, and gives a unified treatment of r?k.
Journal ArticleDOI
Eigenvalues, eigenspaces and distances to subsets
Charles Delorme,J. P. Tillich +1 more
TL;DR: This note shows how to improve and generalize some calculations of diameters and distances in sufficiently symmetrical graphs, by taking all the eigenvalues of the adjacency matrix of the graph into account.
Journal ArticleDOI
A Characterization of Distance-Regular Graphs with DiameterThree
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: In this paper, the authors characterize distance-regular graphs with diameter three by giving an expression for the number of vertices at distance two from each given vertex, in terms of the spectrum of the graph.
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Non-existence of imprimitive Q-polynomial schemes of exceptional type with d=4
Diana R. Cerzo,Hiroshi Suzuki +1 more
TL;DR: This paper will show that the scheme of class 4 does not occur using the integrality conditions of the entries of the first eigenmatrix of X, and that X has exactly one Q-polynomial ordering.
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.