Results 1  10
of
825
Forest matrices around the Laplacian matrix
 Linear Algebra and Its Applications
"... We study the matrices Q k of inforests of a weighted digraph Γ and their connections with the Laplacian matrix L of Γ. The (i, j) entry of Q k is the total weight of spanning converging forests (inforests) with k arcs such that i belongs to a tree rooted at j. The forest matrices, Q k, can be calc ..."
Abstract

Cited by 19 (10 self)
 Add to MetaCart
We study the matrices Q k of inforests of a weighted digraph Γ and their connections with the Laplacian matrix L of Γ. The (i, j) entry of Q k is the total weight of spanning converging forests (inforests) with k arcs such that i belongs to a tree rooted at j. The forest matrices, Q k, can
2.2 The Laplacian Matrix
, 2012
"... 2.1 About these notes These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. The notes written after class way what I wish I said. Be skeptical of all statements in these notes that can be made mathematicall ..."
Abstract
 Add to MetaCart
2.1 About these notes These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. The notes written after class way what I wish I said. Be skeptical of all statements in these notes that can be made mathematically rigorous.
BIPARTITE SUBGRAPHS AND THE SIGNLESS LAPLACIAN MATRIX
 APPL. ANAL. DISCRETE MATH. 5 (2011), 1–13
, 2011
"... For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalised Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subg ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalised Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite
The Third Smallest Eigenvalue Of The Laplacian Matrix
"... Let G be a connected simple graph. The relationship between the third smallest eigenvalue of the Laplacian matrix and the graph structure is explored. For a tree the complete description of the eigenvector corresponding to this eigenvalue is given and some results about the multiplicity of this eige ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Let G be a connected simple graph. The relationship between the third smallest eigenvalue of the Laplacian matrix and the graph structure is explored. For a tree the complete description of the eigenvector corresponding to this eigenvalue is given and some results about the multiplicity
The normalized laplacian matrix and general Randic . . .
, 2010
"... To any graph we may associate a matrix which records information about its structure. The goal of spectral graph theory is to see how the eigenvalues of such a matrix representation relate to the structure of a graph. In this thesis, we focus on a particular matrix representation of a graph, called ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
the normalized Laplacian matrix, which is defined as L = D−1/2(D − A)D−1/2, where D is the diagonal matrix of degrees and A is the adjacency matrix of a graph. We first discuss some basic properties about the spectrum and the largest eigenvalue of the normalized Laplacian. We study graphs that are cospectral
Immanantal Polynomials of Laplacian Matrix of Trees
"... The immanant d (\Delta) associated with the irreducible character Ø of the symmetric group S n , indexed by the partition of n, acting on an n \Theta n matrix A = [a ij ] is defined by d (A) = X oe2Sn Ø (oe) n Y i=1 a ioe(i) : For a tree T on n vertices, let L(T ) denote its Laplacian ..."
Abstract
 Add to MetaCart
Laplacian matrix. Let x be an indeterminate variable and I be the n \Theta n identity matrix. The immanantal polynomial of T corresponding to d is defined as d (xI \Gamma L(T )) = n X k=0 (\Gamma1) k c ;k(T ) x n\Gammak : The coefficients c ;k (T ) admit various algebraic and topological
THE TAU CONSTANT AND THE DISCRETE LAPLACIAN MATRIX OF A Metrized Graph
, 2009
"... We express the tau constant of a metrized graph in terms of the discrete Laplacian matrix and its pseudo inverse. ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
We express the tau constant of a metrized graph in terms of the discrete Laplacian matrix and its pseudo inverse.
Investigation on spectrum of the adjacency matrix and Laplacian matrix of graph Gl
"... Abstract: Let Gl be the graph obtained from Kl by adhering the root of isomorphic trees T to every vertex of Kl, and dk−j+1 be the degree of vertices in the level j. In this paper we study the spectrum of the adjacency matrix A(Gl) and the Laplacian matrix L(Gl) for all positive integer l, and give ..."
Abstract
 Add to MetaCart
Abstract: Let Gl be the graph obtained from Kl by adhering the root of isomorphic trees T to every vertex of Kl, and dk−j+1 be the degree of vertices in the level j. In this paper we study the spectrum of the adjacency matrix A(Gl) and the Laplacian matrix L(Gl) for all positive integer l, and give
A NOTE ON A DISTANCE BOUND USING EIGENVALUES OF THE NORMALIZED LAPLACIAN MATRIX ∗
"... Abstract. Let G be a connected graph, and let X and Y be subsets of its vertex set. A previously published bound is considered that relates the distance between X and Y to the eigenvalues of the normalized Laplacian matrix for G, thevolumesofX and Y, and the volumes of their complements. A counterex ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. Let G be a connected graph, and let X and Y be subsets of its vertex set. A previously published bound is considered that relates the distance between X and Y to the eigenvalues of the normalized Laplacian matrix for G, thevolumesofX and Y, and the volumes of their complements. A
Results 1  10
of
825