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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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Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions
Yu Qing Chen,John Polhill +1 more
TL;DR: In this paper, the authors presented new abelian partial difference sets and amorphic group schemes of both Latin square types and negative Latin square type in certain p-groups.
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Duality in coherent configurations
TL;DR: By introducing a duality operator in coherent algebras of coherent configurations, this work gives a new interpretation to Delsarte's duality theory for association schemes and shows that nonnegative matrices and positive semidefinite matrices are pairs of dual objects.
Posted Content
A characterization of general position sets in graphs
TL;DR: In this paper, it was shown that a vertex subset of a graph is a general position set if and only if the components of the vertex subset are complete subgraphs, the vertices of which form an in-transitive, distance-constant partition of the graph.
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On middle cube graphs
TL;DR: This work completely determines the spectra of the middle cube graphs (eigenvalues and their multiplicities, and associated eigenvectors) in the light of the theory of distance-regular graphs.
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Note: Lattices generated by subspaces in d-bounded distance-regular graphs
Jun Guo,Suogang Gao,Kaishun Wang +2 more
TL;DR: Let @C denote a d-bounded distance-regular graph with diameter d>=2 and @A be a regular strongly closed subgraph of @C, and the empty set @A to be the subspace with diameter -1 in @C.
References
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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.