Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs
Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs
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DOI：
10.1201/b11629
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发表时间：
2012-01
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影响因子：
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通讯作者：
Jason J. Molitierno
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文献类型：
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作者：
Jason J. Molitierno
矩阵理论包括向量范数，矩阵范数，与特征值矩阵位置的谱半径Perron-Frobenius理论矩阵双重随机矩阵广义逆图论基本原理图的运算图和特殊类图的运算图树的连通度序列和极大图平面图和图的高亏格拉普拉斯矩阵的介绍图的矩阵表示矩阵树定理Laplacian图表示的连续形式和能量Laplacian矩阵与网络Laplacian矩阵的谱Laplacian矩阵在某些图运算下的谱Laplacian特征值集的上界小于1和大于1的特征值的分布Grone-Merris猜想极大值（阈值）图的代数连通度作为边权函数的代数连通度图的距离和直径的代数连通度图的代数连通度代数连通度的边密度和等周数平面图的代数连通度代数连通度作为函数亏格k其中k大于1树的Fiedler向量和瓶颈矩阵树的顶点瓶颈矩阵的特征值漂移：I型树中的非同构分支扰动结果应用于树的代数连通度的量化应用：用无限重的边连接两棵树的特征元素树的Laplacian矩阵的子矩阵的谱半径图的瓶颈矩阵构造图的瓶颈矩阵图的Perron分量最小化具有固定围长的图的代数连通性最大化具有固定围长的单圈图的代数连通性应用：代数连通度与割点数图的Laplacian矩阵的子矩阵的谱半径Laplacian矩阵的群逆构造加权树的Laplacian矩阵的群逆作为代数连通度的下界的Zenger函数代数连通度在树中的应用：代数连通度的二阶导数作为边权的函数
Matrix Theory Preliminaries Vector Norms, Matrix Norms, and the Spectral Radius of a Matrix Location of Eigenvalues Perron-Frobenius Theory M-Matrices Doubly Stochastic Matrices Generalized Inverses Graph Theory Preliminaries Introduction to Graphs Operations of Graphs and Special Classes of Graphs Trees Connectivity of Graphs Degree Sequences and Maximal Graphs Planar Graphs and Graphs of Higher Genus Introduction to Laplacian Matrices Matrix Representations of Graphs The Matrix Tree Theorem The Continuous Version of the Laplacian Graph Representations and Energy Laplacian Matrices and Networks The Spectra of Laplacian Matrices The Spectra of Laplacian Matrices Under Certain Graph Operations Upper Bounds on the Set of Laplacian Eigenvalues The Distribution of Eigenvalues Less than One and Greater than One The Grone-Merris Conjecture Maximal (Threshold) Graphs and Integer Spectra Graphs with Distinct Integer Spectra The Algebraic Connectivity Introduction to the Algebraic Connectivity of Graphs The Algebraic Connectivity as a Function of Edge Weight The Algebraic Connectivity with Regard to Distances and Diameters The Algebraic Connectivity in Terms of Edge Density and the Isoperimetric Number The Algebraic Connectivity of Planar Graphs The Algebraic Connectivity as a Function Genus k where k is greater than 1 The Fiedler Vector and Bottleneck Matrices for Trees The Characteristic Valuation of Vertices Bottleneck Matrices for Trees Excursion: Nonisomorphic Branches in Type I Trees Perturbation Results Applied to Extremizing the Algebraic Connectivity of Trees Application: Joining Two Trees by an Edge of Infinite Weight The Characteristic Elements of a Tree The Spectral Radius of Submatrices of Laplacian Matrices for Trees Bottleneck Matrices for Graphs Constructing Bottleneck Matrices for Graphs Perron Components of Graphs Minimizing the Algebraic Connectivity of Graphs with Fixed Girth Maximizing the Algebraic Connectivity of Unicyclic Graphs with Fixed Girth Application: The Algebraic Connectivity and the Number of Cut Vertices The Spectral Radius of Submatrices of Laplacian Matrices for Graphs The Group Inverse of the Laplacian Matrix Constructing the Group Inverse for a Laplacian Matrix of a Weighted Tree The Zenger Function as a Lower Bound on the Algebraic Connectivity The Case of the Zenger Equalling the Algebraic Connectivity in Trees Application: The Second Derivative of the Algebraic Connectivity as a Function of Edge Weight