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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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Journal ArticleDOI
The Hilton–Milner theorem for the distance-regular graphs of bilinear forms
TL;DR: In this paper, the upper bound for the size of a non-trivial intersecting family of n-dimensional subspaces U of V with U ∩ W = 0 is given.
Posted Content
Equitable 2-partitions of Johnson graphs with the second eigenvalue
TL;DR: In this article, the authors studied equitable 2-partitions of the Johnson graphs J(n,w) with a quotient matrix containing the eigenvalue lambda_2(w,n) = (w-2)(n-w2)-2 in its spectrum.
Journal ArticleDOI
A Conjecture of Biggs Concerning the Resistance of a Distance-Regular Graph
Greg Markowsky,J. H. Koolen +1 more
TL;DR: It is proved that the resistance between any two points on a distance-regular graph of valency greater than 2 is bounded by twice the resistanceBetween adjacent points, and the sharp constant for the inequality is given.
Proceedings ArticleDOI
A Grassmannian Packing Based on the Nordstrom-Robinson Code
TL;DR: New families of Grassmannian packings associated with the binary Nordstrom-Robinson code are constructed that find application as highly structured of dictionaries that admit fast algorithms for identifying sparse representations, and in noncoherent wireless communication with multiple antennas.
Journal ArticleDOI
A new distance-regular graph of diameter 3 on 1024 vertices
TL;DR: The dodecacode as discussed by the authors is a nonlinear additive quaternary code of length 12, puncturing it at any of the twelve coordinates, obtaining a uniformly packed code of distance 5.
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.