New Edition! Completely Revised and Updated
Chemical Graph Theory, 2nd Edition is a completely revised and updated edition of a highly regarded book that has been widely used since its publication in 1983. This unique book offers a basic introduction to the handling of molecular graphs - mathematical diagrams representing molecular structures. Using mathematics well within the vocabulary of most chemists, this volume elucidates the structural aspects of chemical graph theory: (1) the relationship between chemical and graph-theoretical terminology, elements of graph theory, and graph-theoretical matrices; (2) the topological aspects of the Hückel theory, resonance theory, and theories of aromaticity; and (3) the applications of chemical graph theory to structure-property and structure-activity relationships and to isomer enumeration. An extensive bibliography covering the most relevant advances in theory and applications is one of the book's most valuable features. This volume is intended to introduce the entire chemistry community to the applications of graph theory and will be of particular interest to theoretical organic and inorganic chemists, physical scientists, computational chemists, and those already involved in mathematical chemistry.
INTRODUCTION. ELEMENTS OF GRAPH THEORY. The Definition of a Graph. Isomorphic Graphs and Graph Automorphism. Walks, Trails, Paths, Distances and Valencies in Graphs. Subgraphs. Regular Graphs. Trees. Planar Graphs. The Story of the Königsberg Bridge Problem and Eulerian Graphs. Hamiltonian Graphs. Line Graphs. Vertex Coloring of a Graph. CHEMICAL GRAPHS. The Concept of a Chemical Graph. Molecular Topology. Hückel Graphs. Polyhexes and Benzenoid Graphs. Weighted Graphs. GRAPH-THEORETICAL MATRICES. The Adjacency Matrix. The Distance Matrix. THE CHARACTERISTIC POLYNOMIAL OF A GRAPH. The Definition of the Characteristic Polynomial. The Method of Sachs for Computing the Characteristic Polynomial. The Characteristic Polynomials of Some Classes of Simple Graphs. The Le Verrier-Faddeev-Frame Method for Computing the Characteristic Polynomial. TOPOLOGICAL ASPECTS OF HÜCKEL THEORY. Elements of Hückel Theory. Isomorphism of Hückel Theory and Graph Spectral Theory. The Hückel Spectrum. Charge Densities and Bond Orders in Conjugated Systems. The Two-Color Problem in Hückel Theory. Eigenvalues of Linear Polyenes. Eigenvalues of Annulenes. Eigenvalues of Möbius Annulenes. A Classification Scheme for Monocyclic Systems. Total p-Electron Energy. TOPOLOGICAL RESONANCE ENERGY. Hückel Resonance Energy. Dewar Resonance Energy. The Concept of Topological Resonance Energy. Computation of the Acyclic Polynomial. Applications of the TRE Model. ENUMERATION OF KEKULÉ VALENCE STRUCTURES. The Role of Kekulé Valence Structures in Chemistry. The Identification of Kekulé Systems. Methods for the Enumeration of Kekulé Structures. The Concept of Parity of Kekulé Structures. THE CONJUGATED-CIRCUIT MODEL. The Concept of Conjugated Circuits. The p-Resonance Energy Expression. Selection of the Parameters. Computational Procedure. Applications of the Conjugated-Circuit Model. Parity of Conjugated Circuits. TOPOLOGICAL INDICES. Definitions of Topological Indices. The Three-Dimensional Wiener Number. ISOMER ENUMERATION. The Cayley Generation Functions. The Henze-Blair Approach. The Pólya Enumeration Method. The Enumeration Method Based on the N-Tuple Code.