Opis: Graph-Theoretical Matrices in Chemistry - Nenad Trinajstic, Sonja Nikolic, Ante Milicevic

Graph-Theoretical Matrices in Chemistry presents a systematic survey of graph-theoretical matrices and highlights their potential uses. This comprehensive volume is an updated, extended version of a former bestseller featuring a series of mathematical chemistry monographs. In this edition, nearly 200 graph-theoretical matrices are included. This second edition is organized like the previous one-after an introduction, graph-theoretical matrices are presented in five chapters: The Adjacency Matrix and Related Matrices, Incidence Matrices, The Distance Matrix and Related Matrices, Special Matrices, and Graphical Matrices. Each of these chapters is followed by a list of references. Among the matrices presented several are novel and some are known only to a few. The properties and potential usefulness of many of the presented graph-theoretical matrices in chemistry have yet to be investigated. Most of the graph-theoretical matrices presented have been used as sources of molecular descriptors usually referred to as topological indices. They are particularly concerned with a special class of graphs that represents chemical structures involving molecules. Due to its multidisciplinary scope, this book will appeal to a broad audience ranging from chemistry and mathematics to pharmacology.Introduction References The Adjacency Matrix and Related Matrices The Vertex-Adjacency Matrix of Simple Graphs The Linear Representation of the Vertex-Adjacency Matrix of Acyclic Structures Labeling Graphs Using the Randic Procedure The Vertex-Adjacency Matrix of Multiple Graphs The Atom-Connectivity Matrix The Bond-Electron Matrix The Edge-Adjacency Matrix The Vertex-Adjacency Matrix of Weighted Graphs The Vertex-Adjacency Matrix of Mobius Graphs The Augmented Vertex-Adjacency Matrix The Edge-Weighted Edge-Adjacency Matrix The Burden Matrix The Vertex-Connectivity Matrix The Edge-Connectivity Matrix The Sum-Vertex-Connectivity Matrix The Sum-Edge-Connectivity Matrix Extended Adjacency Matrices Zagreb Matrices The Huckel Matrix The Laplacian Matrix The Generalized Laplacian Matrix The Augmented Vertex-Degree Matrix Distance-Weighted Adjacency Matrix References Incidence Matrices The Vertex-Edge Incidence Matrix The Edge-Vertex Incidence Matrix The Edge-Cycle Incidence Matrix The Cycle-Edge Incidence Matrix The Vertex-Path Incidence Matrix The Weighted-Hexagon-Kekule-Structure Incidence Matrix References The Distance Matrix and Related Matrices The Standard Distance Matrix or the Vertex-Distance Matrix Generalized Vertex-Distance Matrix The Vertex-Galvez Matrix Combinatorial Matrices Reciprocal Combinatorial Matrices The Edge-Distance Matrix The Vertex-Distance-Complement Matrix The Augmented Vertex-Distance Matrix The Edge-Weighted Vertex-Distance Matrix The Barysz Vertex-Distance Matrix The Complement of the Barysz Vertex-Distance Matrix The Reciprocal Barysz Vertex-Distance Matrix The Reciprocal of the Complement of the Barysz Vertex-Distance Matrix The Complementary Vertex-Distance Matrix The Reciprocal of the Complementary Vertex-Distance Matrix Matrix of Dominant Distances in a Graph The Detour Matrix The Detour-Path Matrix The Detour-Delta Matrix The Edge-Weighted Detour Matrix The Maximum-Minimum Path Matrix The Detour-Complement Matrix The Vertex-Distance Matrix and the Detour Matrix of Complete Graphs and Complete Bipartite Graphs The Vertex-Harary Matrix The Edge-Harary Matrix The Edge-Weighted-Harary Matrix The Modified Edge-Weighted-Harary Matrix Distance-Degree Matrices The Resistance-Distance Matrix Distance/Distance Matrices The Common Vertex Matrix References Special Matrices Adjacency-Plus-Distance Matrices The Distance-Sum-Connectivity Matrix Wiener Matrices The Modified Wiener Matrices The Reverse-Wiener Matrix The Reverse-Detour Matrix Szeged Matrices Reciprocal Szeged Matrices The Unsymmetric Szeged Matrix Cluj Matrices Reciprocal Cluj Matrices The Hosoya Matrix The Path Matrix The All-Path Matrix The Expanded Vertex-Distance Matrices The Quotient Matrices The Random-Walk Markov Matrix Restricted Random-Walk Matrix The Transfer Matrix References Graphical Matrices Construction of Graphical Matrices Numerical Realization of Graphical Matrices A Generalized Procedure for Constructing Graphical Matrices and for Obtaining Their Numerical Representations References Concluding Remarks References Index