Издательство Springer, 1989, -509 pp.Graphs are studied in a wide variety of contexts. This is due to the fact that the con- cept of a graph is both general and convenient. It is convenient because mathematical as well as intuitive notions can often be formulated very easily in terms of symmetric relations; it is general because there are so many symmetric relations on a set. In par- ticular, there is no hope for the classification of all finite graphs in the vein of the classification of, say, all finite fields. However, the situation may change if regularity or symmetry is assumed to exist. Since the ancient determination of the five platonic solids, the study of symmetry and regularity has always been one of the most fascinating aspects of mathematics, and even now there are many challenging problems in this area. One intriguing phenomenon is the fact that quite often arithmetical regularity properties of an object imply the uniqueness of the object, and (often as a consequence of the uniqueness proof) imply the existence of many symmetries, i.e., large automorphism groups. This interplay between regularity and symmetry properties of graphs is the theme of this book. Many regularity properties are naturally expressible in terms of an association scheme, which is by far the most important unifying concept in algebraic combinatorics. Of special interest are two classes of association schemes, those which are polynomial or Q-polynomial. The P-polynomial association schemes (i.e., those with a linear distribution diagram with respect to some relation) are essentially the same objects as distance-regular graphs. As we shall see, the theory of distance-regular graphs has connections to many parts of graph theory, design theory, coding theory, geometry (both finite and Euclidean), and group theory. Indeed, most finite objects of sufficient regularity are closely related to certain distance-regular graphs.Special Regular Graphs Association Schemes Representation Theory Theory of Distance-Regular Graphs Parameter Restrictions for Distance-Regular Graphs Classification of the Known Distance-Regular Graphs Distance-Transitive Graphs Q-polynomial Distance-Regular Graphs The Families of Graphs with Classical Parameters Graphs of Coxeter and Lie Type Graphs Related to Codes Graphs Related to Classical Geometries Sporadic Graphs Tables of Parameters for Distance-Regular Graphs Appendix
Чтобы скачать этот файл зарегистрируйтесь и/или войдите на сайт используя форму сверху.