Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

Matrix Theory Preliminaries. Graph Theory Preliminaries. Introduction to Laplacian Matrices. Algebraic Connectivity. The Fiedler Vector and Bottleneck Matrices for Trees. Bottleneck Matrices for Graphs. The Group Inverse of the Laplacian Matrix.

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• Ciência da Computação
• A matemática discreta
• Algoritmos e estruturas de dados
• Ciência ambiental, engenharia e tecnologia
• Engenharia do controlo automático
• Teoria combinatória e dos grafos

Laplacian Matrix;Algebraic Connectivity;Matrix Theory Preliminaries;Pendant Vertex;Graph Theory Preliminaries;Laplacian Matrices;Introduction to Laplacian Matrices;Cut Vertex;The Algebraic Connectivity;Characteristic Vertex;The Group Inverse of the Laplacian Matrix;Group Inverse;Connected Graph;Nonadjacent Vertices;Fiedler Vector;Perron Vector;Degree Sequence;Matrix Tree Theorem;Bethe Tree;Unweighted Graph;Planar Graph;Weighted Graph;Simple Eigenvalue;Nonnegative Matrices;Unicyclic Graphs;Maximal Planar Graph;Noncomplete Graph;Incidence Matrix;Unweighted Tree;Moore Penrose Inverse