Abstract
We now come to the central topic of the book. The first section may be viewed as a short introduction to the subject. Although we shall develop large parts of the theory of distance-regular graphs independently of Chapter 2, we shall use concepts and results about association schemes for more specialized topics such as Q-polynomial orderings (Chapter 8) and codes in graphs (Chapter 11). In §4.2 we look at various constructions that, given a distance-regular graph, produce a new one. In §4.3 we show how certain conditions on the parameters force the presence of substructures, like lines or Petersen subgraphs. In §4.4 we use the results of Chapter 3 to obtain a characterization by parameters of the two most basic families of distance-regular graphs, the Johnson and Hamming graphs. Chapter 5 contains most of the known conditions on the parameters, Chapter 6 classifies the known distance-regular graphs in various families, Chapter 7 is concerned with distance-transitive graphs, Chapter 8 discusses the consequences of the Q-polynomial property, and the remaining chapters give all examples known to us.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Brouwer, A.E., Cohen, A.M., Neumaier, A. (1989). Theory of Distance-Regular Graphs. In: Distance-Regular Graphs. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74341-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-74341-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-74343-6
Online ISBN: 978-3-642-74341-2
eBook Packages: Springer Book Archive