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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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Strongly closed subgraphs of a distance-regular graph with geometric girth five
Journal ArticleDOI
Statistics and Mathematics: The Appropriate Use of Mathematics within Statistics
TL;DR: The authors argue that statistics can and should use these approaches to become more relevant to the problems that it tackles, not less, and where a corpus of mathematical theory is available which solves the statistical problem at hand, it should be used.
Journal ArticleDOI
Arithmetic completely regular codes
TL;DR: In this article, the authors explore completely regular codes in the Hamming graphs and related graphs and show that the eigenvalues of these codes are in arithmetic progression, i.e., they have the property that the code is in arithmetic progress.
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A characterization of Leonard pairs using the notion of a tail
TL;DR: In this paper, the authors characterize the Leonard pairs using the notion of a tail and call such a pair a Leonard pair on V. This notion is borrowed from algebraic graph theory.
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Chevalley groups of type E7 in the 56-dimensional representation
Nikolai Vavilov,A. Yu. Luzgarev +1 more
TL;DR: In this paper, a detailed computer study of the Chevalley group G(E7, R) on the 56-dimensional minimal module V (7) is presented, and a tabulation of the signs of structure constants for this action is presented.
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.