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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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Book ChapterDOI
Bounds for the Energy of Graphs
TL;DR: In this paper, the graph eigenvalues are labeled in a nonincreasing manner, i.e., λ1≥λ2≥⋯≥ λ n.
Journal ArticleDOI
Fastest mixing Markov chain on graphs with symmetries
TL;DR: In this paper, the authors exploit symmetry of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second largest eigenvalue modulus of the transition probability matrix).
Proceedings ArticleDOI
Constant-rank codes
Maximilien Gadouleau,Zhiyuan Yan +1 more
TL;DR: This paper shows that constant- rank codes are closely related to constant-dimension codes, and investigates the asymptotic behavior of the maximal cardinality of constant-rank codes with given rank weight and minimum rank distance.
Journal ArticleDOI
Symmetric Versus Non-Symmetric Spin Models for Link Invariants
François Jaeger,Kazumasa Nomura +1 more
TL;DR: In this article, it was shown that spin models of odd index are quasi-symmetric, which implies that they are associated with a certain class of symmetric spin models.
Proceedings ArticleDOI
Consensus-based distributed estimation of Laplacian eigenvalues of undirected graphs
TL;DR: This paper presents a novel algorithm for estimating eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system or a wireless sensor network and formulates the problem as a constrained consensus problem.
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.