Expander Families and Cayley Graphs

出版者:OUP USA

作者:Mike Krebs

页数:288

出版时间:2011-11-17

价格:GBP 79.00

装帧:Hardcover

isbn号码:9780199767113

图书标签:计算机科学数学图论GraphsCayley组合Oxford2011

Expander families enjoy a wide range of applications in mathematics and computer science, and their study is a fascinating one in its own right. Expander Families and Cayley Graphs: A Beginner's Guide provides an introduction to the mathematical theory underlying these objects. The central notion in the book is that of expansion, which roughly means the quality of a graph as a communications network. Cayley graphs are certain graphs constructed from groups; they play a prominent role in the study of expander families. The isoperimetric constant, the second largest eigenvalue, the diameter, and the Kazhdan constant are four measures of the expansion quality of a Cayley graph. The book carefully develops these concepts, discussing their relationships to one another and to subgroups and quotients as well as their best-case growth rates. Topics include graph spectra (i.e., eigenvalues); a Cheeger-Buser-type inequality for regular graphs; group quotients and graph coverings; subgroups and Schreier generators; the Alon-Boppana theorem on the second largest eigenvalue of a regular graph; Ramanujan graphs; diameter estimates for Cayley graphs; the zig-zag product and its relation to semidirect products of groups; eigenvalues of Cayley graphs; Paley graphs; and Kazhdan constants. The book was written with undergraduate math majors in mind; indeed, several dozen of them field-tested it. The prerequisites are minimal: one course in linear algebra, and one course in group theory. No background in graph theory or representation theory is assumed; the book develops from scatch the required facts from these fields. The authors include not only overviews and quick capsule summaries of key concepts, but also details of potentially confusing lines of reasoning. The book contains ideas for student research projects (for capstone projects, REUs, etc.), exercises (both easy and hard), and extensive notes with references to the literature.

用户评价

写的太罗嗦了，而且我不喜欢这本书的notation

写的太罗嗦了，而且我不喜欢这本书的notation

写的太罗嗦了，而且我不喜欢这本书的notation

写的太罗嗦了，而且我不喜欢这本书的notation

写的太罗嗦了，而且我不喜欢这本书的notation