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In the last hundred years benzenoid hydrocarbons have constantly attracted the attention of both experimental and theoretical chemists. In spite of the fact that some of the basic concepts of the theory of benzenoid hydrocarbons have their origins in the 19th and early 20th century, research in this area is still in vigorous expansion. The present book provides an outline of the most important current theoretical approaches to benzenoids. Emphasis is laid on the recent developments of these theories, which can certainly be characterized as a significant advance. Em phasis is also laid on practical applications rather than on "pure" theory. The book assumes only some elementary knowledge of organic and physical chemistry and requires no special mathematical training. Therefore we hope that undergraduate students of chemistry will be able to follow the text without any difficulty. Since organic and physical chemists are nowadays not properly acquaint ed lVith the modern theory of benzenoid molecules, we hope that they will find this book both useful and informative. Our book is also aimed at theoretical chemists, especially those concerned with the "topological" features of organic molecules. The authors are indebted to Dr. WERNER SCHMIDT (Ahrensburg, FRG) for valuable discussions. One of the authors (1. G.) thanks the Royal Norwegian Council for Scientific and Industrial Research for financial support during 1988, which enabled him to stay at the University of Trondheim and write the present book. Trondheim, July 1989 Ivan Gutman Sven J. Cyvin Contents Chapter 1 Benzenoid Hydrocarbons .
This text is an attempt to outline the basic facts concerning Kekule structures in benzenoid hydrocarbons: their history, applica­ tions and especially enumeration. We further pOint out the numerous and often quite remarkable connections between this topic and various parts of combinatorics and discrete mathematics. Our book is primarily aimed toward organic and theoretical chemists interested in the enume­ ration of Kekule structures of conjugated hydrocarbons as well as to scientists working in the field of mathematical and computational chemistry. The book may be of some relevance also to mathematicians wishing to learn about contemporary applications of combinatorics, graph theory and other branches of discrete mathematics. In 1985, when we decided to prepare these notes for publication, we expected to be able to give a complete account of all known combi­ natorial formulas for the number of Kekule structures of benzenoid hydrocarbons. This turned out to be a much more difficult task than we initially realized: only in 1986 some 60 new publications appeared dealing with the enumeration of Kekule structures in benzenoids and closely related topics. In any event, we believe that we have collec­ ted and systematized the essential part of the presently existing results. In addition to this we were delighted to see that the topics to·which we have been devoted in the last few years nowadays form a rapidly expanding branch of mathematical chemistry which attracts the attention of a large number of researchers (both chemists and mathematicians).
In this collection from the working group meeting of November 2001, contributors formulate problems, share ideas and approaches, and plan an agenda for future interactions. Their fields included theoretical and applied computer science, statistics, discrete and non-discrete mathematics, chemistry and information science, and the topics centered on
This introductory text in graph theory focuses on partial cubes, which are graphs that are isometrically embeddable into hypercubes of an arbitrary dimension, as well as bipartite graphs, and cubical graphs. Currently, Graphs and Cubes is the only book available on the market that presents a comprehensive coverage of cubical graph and partial cube theories. Many exercises, along with historical notes, are included at the end of every chapter, and readers are encouraged to explore the exercises fully, and use them as a basis for research projects. The prerequisites for this text include familiarity with basic mathematical concepts and methods on the level of undergraduate courses in discrete mathematics, linear algebra, group theory, and topology of Euclidean spaces. While the book is intended for lower-division graduate students in mathematics, it will be of interest to a much wider audience; because of their rich structural properties, partial cubes appear in theoretical computer science, coding theory, genetics, and even the political and social sciences.
Even high-speed supercomputers cannot easily convert traditional two-dimensional databases from chemical topology into the three-dimensional ones demanded by today's chemists, particularly those working in drug design. This fascinating volume resolves this problem by positing mathematical and topological models which greatly expand the capabilities of chemical graph theory. The authors examine QSAR and molecular similarity studies, the relationship between the sequence of amino acids and the less familiar secondary and tertiary protein structures, and new topological methods.
This handbook examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, this second edition presents full proofs of many important results as well as up-to-date research and conjectures. It illustrates applications of graph products in several areas and contains well over 300 exercises. Supplementary material is available on the book's website.
YU ISSN 0561-7332 TABLE DES MATIERES 1. M. Budineevie: Oscillation of a second order neutral difference equation 1 2. W. C. Simi, P. C. B. Lam, I. Gutman: Wiener number of hexagonal bitra,peziums and trapeziums 9 3. S. Todoreevie: Ernbeddabiliiy of K x C into X 27 4. W. Junde, E. Pap, L. Ranglu, Q. \\Tenho: Swartz 's Orlicz-Peitis theorem for operators 37 5. Mileva Prvanovie: Locally decomposable Riemannian Mani fold endowed with SOPTC SE,Tili-symmetric F-co-nnection 15 6. D. Herceg: On a discrete analogue for, singularly perturbed BVP 57 7. Olga. Had2ie: Fixed point theorems in inetrizable H-spaces 75 8. H. C. Howard, V. Marie: Regularity and nonoscillation of solutions of second order linear differential equations 85 9. M. Marjanovie, I. Gutman: A distance-based graph invariant related to the Wiener and Szeged numbers 99 Ово дело је лиценцирано под условима лиценце Creative Commons - Attribution-Noncommercial-No Derivative Works 3.0 Serbia http://creativecommons.org/licenses/by-nc-nd/3.0/rs/deed.en
Solved and Unsolved Problems of Structural Chemistry introduces new methods and approaches for solving problems related to molecular structure. It includes numerous subjects such as aromaticity-one of the central themes of chemistry-and topics from bioinformatics such as graphical and numerical characterization of DNA, proteins, and proteomes. It a
Valence bond (VB) theory, which builds the descriptions of molecules from those of its constituent parts, provided the first successful quantum mechanical treatments of chemical bonding. Its language and concepts permeate much of chemistry, at all levels. Various modern formulations of VB theory represent serious tools for quantum chemical studies of molecular electronic structure and reactivity. In physics, there is much VB-based work (particularly in semi-empirical form) on larger systems. Importance of TopicThe last decade has seen significant advances in methodology and a vast increase in the range of applications, with many new researchers entering the field.Why This TitleValence Bond Theory succeeds in presenting a comprehensive selection of contributions from leading valence bond (VB) theory researchers throughout the world. It focuses on the vast increase in the range of applications of methodology based on VB theory during the last decade and especially emphasizes recent advances.