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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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Some algebra related to $P$-and $Q$-polynomial association schemes
TL;DR: In this paper, the authors introduced a mild generalization of a Leonard pair called a tridiagonal pair, which is the same thing as a tridimensional pair such that for each transformation all eigenspaces have dimension one.
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Vertex primitive graphs of order containing a large prime factor
TL;DR: This paper and [16] together give a complete classification of all vertex primitive symmetric graphs of order kp, where k is not a prime.
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Improving diameter bounds for distance-regular graphs
TL;DR: It is shown that if d ≥ 2j and cj > 1 then c2j-1 > cj holds and improvements on diameter bounds are given by applying this inequality.
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Eigenpolytopes of Distance Regular Graphs
TL;DR: In this paper, it was shown that the eigenpolytope associated to the second largest eigenvalue of a convex hull of a set of vectors is isomorphic to the 1-skeleton of a distance regular graph.
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Splitting fields of association schemes
TL;DR: The splitting field K of a commutative association scheme is the extension of the rationals by the adjunction of all eigenvalues of the association scheme if the Krein parameters are all rational, then the eigen values are contained in a cyclotomic number field.
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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.
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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.