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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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On the equivalence between real mutually unbiased bases and a certain class of association schemes
TL;DR: The main results of this paper establish an equivalence between sets of real mutually unbiased bases and 4-class cometric association schemes which are both Q-bipartite and Q-antipodal.
Proceedings ArticleDOI
On error control codes for random network coding
Rudolf Ahlswede,H. Aydinian +1 more
TL;DR: This paper considers codes correcting insertions/deletions (dimension enlargement and dimension reduction respectively) in noncoherent random network coding, and bounds and constructions for those codes are presented.
Journal ArticleDOI
Circulant graphs: recognizing and isomorphism testing in polynomial time
TL;DR: In this article, an algorithm was constructed for recognizing the circulant graphs and finding a canonical labeling for them in polynomial time, and the consistency of the algorithm was based on a new result on the structure of Schur rings over a finite cyclic group.
Journal ArticleDOI
Graphs cospectral with distance-regular graphs
Willem H. Haemers,E. Spence +1 more
TL;DR: In this article, the authors determined all graphs with the spectrum of a distance-regular graph with at most 30 vertices, except possibly for the Taylor graph on 28 vertices.
Journal ArticleDOI
Finite distance-transitive generalized polygons
TL;DR: In this article, it was shown that every group with an irreducible rank 2 BN-pair arises from a group of Lie type, and that all groups with an automorphism group acting distance-transitively on the set of points can be classified as simple groups.
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.