Explorations in Algebraic Graph Theory by Chris Godsil, Rob Beezer
About this book :-
Algebraic graph theory is a fascinating subject concerned with the interplay between algebra and graph theory. Algebraic tools can be used to give surprising and elegant proofs of graph theoretic facts, and there are many interesting algebraic objects associated with graphs. Algebraic Graph Theory is Sage is an ideal place to experiment with the relevant mathematics: graph theory, linear algebra and permutation groups, along with combinatorics generally. This book will provide a useful introduction for the student or researcher, while simultaneously aiding the continual improvement of Sage itself.
It covers key concepts like adjacency and incidence matrices, spectral graph methods, and connections between algebraic structures and graphs.
It examines topics like graph eigenvalues, symmetries, invariants, and homomorphisms through a self-contained, example-rich approach. It’s aimed at upper-level undergraduates, graduate students, and researchers, requiring only basic linear algebra and elementary group theory.
This book is primarily aimed at graduate students and researchers in graph theory, combinatorics, or discrete mathematics in general. However, all the necessary graph theory is developed from scratch, so the only pre-requisite for reading it is a first course in linear algebra and a small amount of elementary group theory. It should be accessible to motivated upper-level undergraduates. Chris Godsil is a full professor in the Department of Combinatorics and Optimization at the University of Waterloo. It tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth.
Book Detail :-
Title:
Explorations in Algebraic Graph Theory by Chris Godsil, Rob Beezer
Publisher:
University of Puget Sound
Year:
2010
Pages:
400
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
GNU
Amazon:
Amazon
About Author :-
The author
Chris Godsil
is Professor at Department of Combinatorics and Optimization, University of Waterloo, Robert A. Beezer is a Professor of Mathematics at the University of Puget Sound, where he has been on the faculty since 1984. In addition to his teaching at the University of Puget Sound, he has made sabbatical visits to the University of the West Indies (Trinidad campus) and the University of Western Australia. He has also given several courses in the Master’s program at the African Institute for Mathematical Sciences, South Africa. He has been a Sage developer since 2008. He teaches calculus, linear algebra and abstract algebra regularly, while his research interests include the applications of linear algebra to graph theory.
Book Contents :-
1. Getting Started
2. First Projects
3. Cayley Graphs
4. Distance-Regular Graphs
5. One-Factors of K6
6. The Hoffman-Singleton Graph
7. Matrices
8. Polynomials and Power Series
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