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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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Generalized Designs on Graphs: Sampling, Spectra, Symmetries
TL;DR: Spherical designs are finite sets of points on the sphere with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on the whole sphere as mentioned in this paper.
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A distance regular graph with intersection array (21, 16, 8; 1, 4, 14) does not exist
TL;DR: It is shown that a distance regular graph Γ with intersection array (21, 16, 8; 1, 4, 14) does not exist and the proof uses algebraic properties of a positive semidefinite matrix related to the neighbourhood of a vertex of Γ.
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Higmanian rank-5 association schemes on 40 points
TL;DR: Zivav et al. as discussed by the authors gave a comprehensive enumeration of imprimitive association schemes on 40 points with 4 classes which are proper class II in the sense of [Hig95] and showed that there is no scheme for the fourth set.
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Large {0,1,…,t}-cliques in dual polar graphs
Ferdinand Ihringer,Klaus Metsch +1 more
TL;DR: The largest, second largest, and smallest eigenvalue of the graphs which have the generators of a polar space as vertices and where two generators are adjacent if and only if they meet in codimension at least t + 1 are determined.
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Propelinear 1-Perfect Codes From Quadratic Functions
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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.