Graph-Theoretical Matrices in Chemistry  book cover
1st Edition

Graph-Theoretical Matrices in Chemistry

ISBN 9781498701150
Published April 22, 2015 by CRC Press
160 Pages 52 B/W Illustrations

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Book Description

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.

Table of Contents


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


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

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

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

Graphical Matrices
Construction of Graphical Matrices
Numerical Realization of Graphical Matrices
A Generalized Procedure for Constructing Graphical Matrices and for Obtaining Their Numerical Representations

Concluding Remarks

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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, Croatia

Sonja Nikolić, PhD, The Rugjer Bošković Institute, Zagreb, Croatia

Nenad Trinajstić, PhD, fellow of the Croatian Academy of Sciences and Arts, The Rugjer Bošković Institute, Zagreb, Croatia