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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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An Action of the Tetrahedron Algebra on the Standard Module for the Hamming Graphs and Doob Graphs
TL;DR: An action of the tetrahedron algebra is displayed on the standard module for any Hamming graph or Doob graph using some results of Brian Hartwig concerning tridiagonal pairs of Krawtchouk type.
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Affine distance-transitive groups with alternating or symmetric point stabiliser
TL;DR: All finite graphs which admit a distance-transitive, primitive, affine automorphism groupG such that a point stabilizer inG is an alternating or symmetric group (modulo scalars) is determined.
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Packing radius, covering radius, and dual distance
TL;DR: In this article, proofs relying solely on the orthogonality relations of Krawtchouk (1929), Lloyd, and, more generally, Krawchouk-adjacent orthogonal polynomials are derived and upper bounds on the minimum distance of formally self-dual binary codes are derived.
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Application of some graph invariants to the analysis of multiprocessor interconnection networks
TL;DR: In this paper, it was shown that the number of connected graphs with a bounded tightness is finite and that the tightness of the second type is a relevant graph invariant.
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On a Conjecture of Bannai and Ito: There are Finitely Many Distance-regular Graphs with Degree 5, 6 or 7
Jack H. Koolen,Vincent Moulton +1 more
TL;DR: This paper proves that the Bannai–Ito conjecture holds for distance-regular graphs with degrees 5–7.
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.