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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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Book ChapterDOI
Invariant semidefinite programs
Christine Bachoc,Dion Gijswijt,Dion Gijswijt,Alexander Schrijver,Alexander Schrijver,Frank Vallentin +5 more
TL;DR: In this paper, the basic theory of semidefinite programs with symmetry is described and applications from coding theory, combinatorics, geometry, and polynomial optimization are discussed.
Dissertation
Independent Sets and Eigenspaces
TL;DR: The methods developed for covering array graphs apply to the EKR theorem, and a proof of the characterization of the extremal cases for the q-analogue when v = 2k is provided; no such proof has appeared before.
Journal ArticleDOI
Eigenvalues and edge-connectivity of regular graphs
TL;DR: In this paper, it was shown that if the second largest eigenvalue of a d-regular graph G is less than ρ ( d ), then G is 2 -edge-connected.
Journal ArticleDOI
Characterizing distance-regularity of graphs by the spectrum
TL;DR: The distance-regular Ivanov-lvanov-Faradjev graph is characterized from the spectrum, and the known results on cospectral graphs of the Hamming graphs, and of all distance- regular graphs on at most 70 vertices are surveyed.
Journal ArticleDOI
Portraits of complex networks
TL;DR: A method for characterizing large complex networks is proposed by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks.
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.