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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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The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two
Mark S. MacLean,Paul Terwilliger +1 more
TL;DR: The structure of W is described and it is shown W has a basis E"iv(i@?S), where E"i denotes the primitive idempotent of A associated with @q"i and where the set S is {1,2,...,d-1}@?{d+1,d+ 2,...,D-1}) and this basis is orthogonal (with respect to the Hermitian dot product).
Journal ArticleDOI
Distance regularity in buildings and structure constants in Hecke algebras
TL;DR: In this paper, a generalised notion of distance regularity in buildings is introduced, and a combinatorial formula for the cardinalities of intersections of generalised spheres is developed.
Journal ArticleDOI
Rank 5 association schemes and triality
TL;DR: The classical triality associated with the groups O + 8 ( q ) provides a family of symmetric association schemes with rank 3, corank 2 parabolics, and sporadic examples associated with groups L 3 (4), U 6 (2) and U 3 (5) as mentioned in this paper.
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Relative difference sets fixed by inversion and Cayley graphs
Yu Qing Chen,Cai Heng Li +1 more
TL;DR: This work presents a construction of a (30, 2, 29, 14)-relative difference set fixed by inversion in the smallest finite simple group--the alternating group A5, which is the first example known of relative difference sets in the finite simple groups with a non-trivial forbidden subgroup.
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.