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Introduction Problems of Antiquity Famous Problems Illustrious Problems Hilbert Problems P versus NP On Unsolved Problems References and Notes Mathematical Chemistry Discrete Mathematics and Chemistry Partial Order Enumeration of Kekule Valence Structures Graph Theory Chemical Nomenclature Molecular Descriptors Canonical Labeling of Vertices Counting of Paths Experimental Mathematics References and Notes Graph Theory and Chemistry Unfamiliarity with Graph Theory On HMO, the Huckel Molecular Orbital Theory The Story of Isospectral Graphs The Difference in HMO and PPP Bond Orders Graphene Edge References and Notes Characteristic Polynomial On Characteristic Polynomial On Construction of the Characteristic Polynomial Fermat’s Last Theorem Common Eigenvalues Chemical Mathematics Revisiting the Characteristic Polynomial On Factoring of Characteristic Polynomial Symmetric Function and Newton Identities Summary References and Notes Structure-Activity Two Cultures Qualitative Regression Analysis QSAR versus \"QSAR\" On Quantitative Characterization of Molecular Structure The Criticism That Is Not Highly Collinear Descriptors: The Problem That Is Not The Single Equation Fallacy References and Notes Molecular Descriptors Structure Descriptors The Connectivity Index Topological Indices Complex Biomolecular Networks and the Connectivity Index 1 Joseph Boscovic Desiderata for Molecular Descriptors Higher-Order Connectivity Indices Molecular ID Numbers Recent Modification of the Higher-Order Connectivity Indices Variations of the Connectivity Index On Characterization of Hetero-Atoms The Variable Connectivity Index Surprise, Surprise The Structure-Structure Space References and Notes Partial Ordering Searching for Regularities in Structure-Property Data On Characterization of Molecular Structures Partial Ordering 13C Chemical Shifts Sums in Alkanes Study of Proteome Maps Using Partial Ordering References and Notes Novel Molecular Matrices Novel Molecular Descriptors Novel Matrices in Chemistry Generalized Distance Matrices Ring Closure Matrix Spanning Trees Canonical Labels for Graphs Canonical Labels for Adamantane Walk Above Code for Polycyclic Graphs Ring Closure Matrix of Adamantane References and Notes On Highly Similar Molecules Search for Structurally Similar Molecules Molecular Descriptors for Screening Combinatorial Libraries Generalized Connectivity Indices Connectivity Index (HD) References and Notes Aromaticity Revisited Conjugated Circuits Resonance Energies In Search of a Generalized Huckel 4n + 2 Rule On Classification of Polycyclic Conjugated Compounds References and Notes Clar Aromatic Sextet Introduction Qualitative Clar Aromatic Sextet Theory Clar Aromatic Sextet Revisited Pauling Bond Orders Ring Bond Orders Quantitative Aromatic Sextet Theory Resonance Graphs References and Notes Renormalization in Chemistry Continuum versus Discrete Models Ring Currents via the Conjugated Circuits Model Normalization of Ring Currents Renormalization of Ring Currents Concluding Remarks Anecdotes Plagiarism That Is Not References and Notes Graphical Bioinformatics Characterization versus Indexing Milestones of Graphical Bioinformatics Spectral Representation of DNA Four-Color 2-D Maps of DNA Similarities and Dissimilarities among the DNA Sequences Is a Four-Color DNA Map a Useful Novelty? Amino Acid Adjacency Matrix Decagonal Isometric Matrix On the Sequence Alignment Problem Amino Acid Sequential Matrix Computer Program for the Exact Solution of the Protein Alignment Problem References and Notes Beauties and Sleeping Beauties in Science Sleeping Beauties Revisited On Beauty in Science Five Sleeping Beauties Aromaticity and Conjugation 4n + 2 and 4n Rule for Polycyclic Conjugated Systems Orthogonal Molecular Descriptors Variable Connectivity Index Proteome Maps: Order or Chaos? Graphical Alignment of Proteins Sleeping Giants Summary Apology Acknowledgments References and Notes Appendix 1: Early Hostility toward Chemical Graph Theory Appendix 2: Editorial Alert to Reviewers on Graph Theoretical Manuscripts Appendix 3: Letter Relating to the Calculation of the Symmetry of a Graph Appendix 4: On Detection of the Illegal Deck of Cards for Graph Reconstruction Appendix 5: Solution to Halmos Handshake Problem Appendix 6: The First Page of the Book of Euclid Appendix 7: Full Quote of Immanuel Kant Appendix 8: Construction of Canonical Labels for Diamantane Appendix 9: Twelve Different Canonical Labelings of Diamantane Appendix 10: The Eigenvalues and Eigenvectors of Hexatriene Appendix 11: The Coefficients of All Antisymmetrical Molecular Orbitals of the Tetracene Derivative C20H14 Appendix 12: Halogen Compounds and Their Boiling Points Appendix 13: \"News and Views\" on Chemical Topology from Nature, November 15, 1974 Appendix 14: Conjugated Circuits for the Remaining Five Symmetry Nonequivalent Kekule Valence Structures of Coronene Appendix 15: Hostile Reports of Anonymous Referees on Novelty in Graphical Bioinformatics Appendix 16: The Computer Program for Exact Pairwise Protein Alignment Appendix 17: An Input and Output of the Program VESPA Appendix 18: List of Problems of Structural Chemistry Presented in This Book Appendix 19: Rigorous Definitions and Descriptions of a Selection of Mathematical Concepts of Discrete Mathematics

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