Graph-theoretical Matrices in Chemistry

Graph-theoretical Matrices in Chemistry

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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 more

Product details

  • Paperback
  • 155.96 x 233.93mm
  • CRC Pr I Llc
  • English
  • 1138894281
  • 9781138894280

About Dusanka Janezic

Dušanka Janežič, PhD, University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies, Koper, Slovenia Ante Miličević, PhD, The Institute for Medical Research and Occupational Health, Zagreb, CroatiaSonja Nikolić, PhD, The Rugjer Bošković Institute, Zagreb, CroatiaNenad Trinajstić, PhD, fellow of the Croatian Academy of Sciences and Arts, The Rugjer Bošković Institute, Zagreb, Croatiashow more

Table of contents

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 Randić 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 Möbius 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 Hückel 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-Kekulé-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 Indexshow more