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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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Closed‐form formulas for Kirchhoff index
TL;DR: In this paper, the authors find closed-form expressions for the Kirchhoff index of certain connected graphs using Foster's theorems, random walks, and the superposition principle.
Posted Content
Reduction of symmetric semidefinite programs using the regular*-representation
TL;DR: In this paper, a low-order matrix representation of the commutant ring of the matrix algebra generated by permutation matrices is proposed to reduce the size of semidefinite programming problems on which a permutation group is acting.
Journal ArticleDOI
Eigenvalues and perfect matchings
TL;DR: In this article, the authors give sufficient conditions for existence of a perfect matching in a graph in terms of the eigenvalues of the Laplacian matrix, and also show that a distance-regular graph of degree k is k-edge-connected.
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Completely regular codes
TL;DR: This paper shows that the basic theory—including Lloyd's theorem—can be obtained very elegantly by methods inspired from the theory of distance regular graphs.
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Regular graphs with four eigenvalues
TL;DR: In this article, the authors studied connected regular graphs with four distinct eigenvalues, and properties and feasibility conditions of the eigen values were given, as well as some uniqueness and nonexistence results.
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.