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Characterizing the second smallest eigenvalue of the normalized Laplacian of a tree
, 2014
"... iv ..."
Asymptotic behaviour of the number of Eulerian circuits
"... We determine the asymptotic behaviour of the number of Eulerian circuits in undirected simple graphs with large algebraic connectivity (the secondsmallest eigenvalue of the Laplacian matrix). We also prove some new properties of the Laplacian matrix. 1 ..."
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Cited by 4 (1 self)
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We determine the asymptotic behaviour of the number of Eulerian circuits in undirected simple graphs with large algebraic connectivity (the secondsmallest eigenvalue of the Laplacian matrix). We also prove some new properties of the Laplacian matrix. 1
ftp ejde.math.txstate.edu (login: ftp) ON THE SECOND EIGENVALUE OF A HARDYSOBOLEV OPERATOR
"... Abstract. In this note, we study the variational characterization and some properties of the second smallest eigenvalue of the HardySobolev operator Lµ: = −∆p − µxp with respect to an indefinite weight V (x). 1. ..."
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Abstract. In this note, we study the variational characterization and some properties of the second smallest eigenvalue of the HardySobolev operator Lµ: = −∆p − µxp with respect to an indefinite weight V (x). 1.
Maximum algebraic connectivity augmentation is NPhard
 Oper. Res. Lett
"... The algebraic connectivity of a graph, which is the secondsmallest eigenvalue of the Laplacian of the graph, is a measure of connectivity. We show that the problem of adding a specified number of edges to an input graph to maximize the algebraic connectivity of the augmented graph is NPhard. ..."
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Cited by 20 (0 self)
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The algebraic connectivity of a graph, which is the secondsmallest eigenvalue of the Laplacian of the graph, is a measure of connectivity. We show that the problem of adding a specified number of edges to an input graph to maximize the algebraic connectivity of the augmented graph is NPhard.
New spectral methods for ratio cut partition and clustering
 IEEE TRANS. ON COMPUTERAIDED DESIGN
, 1992
"... Partitioning of circuit netlists is important in many phases of VLSI design, ranging from layout to testing and hardware simulation. The ratio cut objective function [29] has received much attention since it naturally captures both mincut and equipartition, the two traditional goals of partitionin ..."
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Cited by 295 (17 self)
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of partitioning. In this paper, we show that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost. We also demonstrate that fast Lanczostype methods for the sparse symmetric eigenvalue problem are a robust basis
Hypergraph Markov Operators, Eigenvalues and Approximation Algorithms
, 2014
"... The celebrated Cheeger’s Inequality [AM85, Alo86] establishes a bound on the expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency matrix (and other related matrices) of graphs. It ha ..."
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Cited by 4 (2 self)
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Cheegertype inequality for hypergraphs, relating the second smallest eigenvalue of this operator to the expansion of the hypergraph. We bound other hypergraph expansion parameters via higher eigenvalues of this operator. We give bounds on the diameter of the hypergraph as a function of the second
The Laplacian Spread of a Tree
 Discrete Mathematics and Theoretical Computer Science
"... The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we show that the star is the unique tree with maximal Laplacian spread among all trees of given order, and the path i ..."
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Cited by 6 (1 self)
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The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we show that the star is the unique tree with maximal Laplacian spread among all trees of given order, and the path
Cooperative Control of multiple Autonomous Vehicles
"... Abstract — Maximization of the second smallest eigenvalue of the graph Laplacian has recently been studied in the field of cooperative control. Instead of the second smallest eigenvalue, we design a gradientbased control law for multiple agents to maximize an arbitrary nonzero eigenvalue. The gradi ..."
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Abstract — Maximization of the second smallest eigenvalue of the graph Laplacian has recently been studied in the field of cooperative control. Instead of the second smallest eigenvalue, we design a gradientbased control law for multiple agents to maximize an arbitrary nonzero eigenvalue
A Spectral Lower Bound for the Treewidth of a Graph and its Consequences
"... Abstract. We give a lower bound for the treewidth of a graph in terms of the second smallest eigenvalue of its Laplacian matrix. We use this lower bound to show that the treewidth of a ddimensional hyper cube is at least j 3\Delta 2d ..."
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Abstract. We give a lower bound for the treewidth of a graph in terms of the second smallest eigenvalue of its Laplacian matrix. We use this lower bound to show that the treewidth of a ddimensional hyper cube is at least j 3\Delta 2d
The Laplacian spread of tricyclic graphs
 2009), Research Paper
"... The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs with max ..."
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The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs
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