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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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Combinatorial representations of Coxeter groups over a field of two elements
Hau-wen Huang,Chih-wen Weng +1 more
TL;DR: In this paper, a simply-laced Coxeter group with n generators was constructed, and an n-dimensional representation of W over the finite field F 2 of two elements was constructed.
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Taut distance-regular graphs and the subconstituent algebra
Mark S. MacLean,Paul Terwilliger +1 more
TL;DR: Three characterizations of the taut condition of the bipartite distance-regular graph @C are obtained, each of which involves the local eigenvalues or the above T-modules.
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The Generalized Terwilliger Algebra and its Finite-dimensional Modules when d = 2
TL;DR: In this paper, it was shown that T is the associative C-algebra with identity generated by C and C* subject to the analogues of Terwilliger's triple product relations.
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New strongly regular graphs from finite geometries via switching
TL;DR: The authors showed that the strongly regular graph on non-isotropic points of one type of the polar spaces of type U (n, 2 ), O ( n, 3 ),O ( n, 3 ), O( n, 5 ), and O + (n, 3 ), for n ≥ 6, is not determined by its parameters.
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There Exists no Distance-regular Graph with Intersection Array (5,4,3; 1,1,2)
TL;DR: A short, computer-free proof that there is no graph with these parameters, which is the smallest unsolved case 1.
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.