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Distance-Regular Graphs
TLDR
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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On graphs whose smallest eigenvalue is at least − 1 − √2
Renee Woo,Arnold Neumaier +1 more
TL;DR: The main result of as discussed by the authors is that if the smallest eigenvalue of a graph H exceeds a fixed number larger than the smallest root (≈ − 2.4812) of the polynomial x3 + 2x2 − 2x − 2X − 2, and if every vertex of H has sufficiently large valency, then H is at least − 1 − √ 2 and the structure of H is completely characterized through a new generalization of line graphs.
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Root shadow spaces
Aaron Cohen,Gábor Ivanyos +1 more
TL;DR: The results generalize earlier geometric point-line characterizations of certain spherical buildings as well as Timmesfeld's characterization of abstract root subgroups to characterization of root shadow spaces of buildings whose types correspond to Dynkin diagrams.
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A characterization of Grassmann graphs
TL;DR: A characterization of Γ(e, q, n) in terms of parameters is obtained provided that e ≠ 2, n − 2, 12n, 12(n ± 1) and (e ≠ 12( n±2) if q = 3) and it is shown that these Grassmann graphs are uniquely determined as distance-regular graphs by their intersection arrays.
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Combinatorial Designs with Two Singular Values II. Partial Geometric Designs
Edwin van Dam,Edward Spence +1 more
TL;DR: In this article, the authors study combinatorial designs whose incidence matrix has two distinct singular values and give new characterization results, and enumerate, partly by computer, all small ones.
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Computing Isotypic Projections with the Lanczos Iteration
TL;DR: This paper shows how the isotypic subspaces of a representation are viewed as the eigenspaces of a symmetric linear transformation and this approach gives rise to an efficient isotypeic projection method for permutation representations of distance transitive graphs and the symmetric group.
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.