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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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An inequality on the cosines of a tight distance-regular graph
TL;DR: In this article, the authors investigated the relationship between equality being attained and the existence of dual bipartite Q -polynomial structures on a distance-regular graph with diameter d⩾3 and obtained an inequality involving the first, second and third cosines associated with θ.
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The twisted Grassmann graph is the block graph of a design
TL;DR: In this article, it was shown that the twisted Grassmann graph constructed by Van Dam and Koolen is the block graph of the design constructed by Jungnickel and Tonchev.
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Sparse topologies with small spectrum size
TL;DR: This paper presents graphs, for any n, for which the product of their vertex degree and the number of different eigenvalues is small and it is known that load balancing can be performed on such graphs in a small number of steps.
Posted Content
A new approach to the theory of classical hypergeometric polynomials
José Marco,Javier Parcet +1 more
TL;DR: In this paper, the authors present a unified approach to the spectral analysis of an hypergeometric type operator whose eigenfunctions include the classical orthogonal polynomials.
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More on block intersection polynomials and new applications to graphs and block designs
TL;DR: A new method of bounding the size of a clique in an edge-regular graph with given parameters is obtained, which can improve on the Hoffman bound when applicable, and a new method for studying the possibility of agraph with given vertex-degree sequence being an induced subgraph of a strongly regular graph withgiven parameters is found.
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.