On graphs with equal algebraic and vertex connectivity
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In this paper, it was shown that the equality 1/Z(L#)=a(G) does not necessarily imply that 1/z(L #) satisfies the vertex connectivity constraint.About:
This article is published in Linear Algebra and its Applications.The article was published on 2002-01-15 and is currently open access. It has received 68 citations till now. The article focuses on the topics: Bound graph.read more
Citations
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Old and new results on algebraic connectivity of graphs
TL;DR: A survey of algebraic connectivity of a graph G is given in this paper, where the second smallest eigenvalue of the Laplacian of the graph G, denoted a(G), is considered.
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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.
Posted Content
The Laplacian eigenvalues of graphs: a survey
TL;DR: The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0, 1) adjacency matrix as discussed by the authors, and it has been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning.
A Survey of Automated Conjectures in Spectral Graph Theory
TL;DR: In this article, the authors present a survey and a discussion of the results about graph eigenvalues that were first conjectured using computer programs, such as GRAPH, Graffiti, Ingrid, newGRAPH and AutoGraphiX.
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A survey of automated conjectures in spectral graph theory
TL;DR: A survey and a discussion of results about graph eigenvalues first conjectured, and in some cases proved, using computer programs, such as GRAPH, Graffiti, Ingrid, newGRAPH and AutoGraphiX are presented.
References
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Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
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Algebraic connectivity of graphs
Book
Non-negative Matrices and Markov Chains
TL;DR: Finite Non-Negative Matrices as mentioned in this paper are a generalization of finite stochastic matrices, and finite non-negative matrices have been studied extensively in the literature.
Book
Generalized inverses of linear transformations
TL;DR: In this article, the Moore-Penrose or generalized inverse has been applied to the theory of finite Markov chains, and applications of the Drazin inverse have been discussed.