Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.
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1 of 3 people found the following review helpful:
3.0 out of 5 stars
graduate or post graduate text,
By R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: Distance Regular Graphs (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge) (Hardcover)
I really can't give this very high marks because it isn't a teaching text but more or less a theorems and proof type text
that is really difficult, dull and card board. If you have a graduate class in graphs with this as a text, drop it and wait for a better teacher. I'm not saying that the book doesn't contain a lot of important material, just that it might take more than a semester to read the book and understand it without the author having tried to help you understand.
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