algebraic graph theory 2e norman biggs [pdf]
Algebraic Graph Theory (2E) by Norman L. Biggs
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About this book :-
Algebraic Graph Theory (2E)
Norman L. Biggs.
This book is concerned with the use of algebraic techniques in the study of graphs. We aim to translate properties of graphs into algebraic properties and then, using the results and methods of algebra, to deduce theorems about graphs.
The exposition which we shall give is not part of the modern functorial approach to topology, despite the claims of those who hold that, since graphs are one-dimensional spaces, graph theory is merely one-dimensional topology. By that definition, algebraic graph theory would consist only of the homology of 1-complexes.
But the problems dealt with in graph theory are more delicate than those which form the substance of algebraic topology, and even if these problems can be generalized to dimensions greater than one, there is usually no hope of a general solution at the present time. Consequently, the algebra used in algebraic graph theory is largely unrelated to the subject which has come to be known as homological algebra.
Book Detail :-
Title: Algebraic Graph Theory
Author(s): Norman L. Biggs
Publisher: Cambridge University Press
Series: Cambridge Tracts in Mathematics
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About Author :-
The author Norman L. Biggs was a lecturer at University of Southampton, lecturer then reader at Royal Holloway, University of London, and Professor of Mathematics at the London School of Economics. He has been on the editorial board of a number of journals, including the Journal of Algebraic Combinatorics. He has been a member of the Council of the London Mathematical Society.
He has written 12 books and over 100 papers on mathematical topics, many of them in algebraic combinatorics and its applications. He became Emeritus Professor in 2006 and continue to teach History of Mathematics in Finance and Economics for undergraduates. He is also Vice-President of the British Society for the History of Mathematics.
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Book Contents :-
Norman L. Biggs, E. Keith Lloyd, Robin J. Wilson
cover the following topics.
Part-1 LINEAR ALGEBRA IN GRAPH THEORY
2. The spectrum of a graph
3. Regular graphs and line graphs
4. The homology of graphs
5. Spanning trees and associated structures
7. Determinant expansions
Part-2 COLOURING PROBLEMS
8. Vertex-colourings and the spectrum
9. The chromatic polynomial
10. Edge-subgraph expansions
11. The logarithmic transformation
12. The vertex-subgraph expansion
13. The Tutte polynomial
14. The chromatic polynomial and spanning trees
Part-3 SYMMETRY AND REGULARITY OF GRAPHS
15. General properties of graph automorphisms
16. Vertex-transitive graphs
17. Symmetric graphs
18. Trivalent symmetric graphs
19. The covering-graph construction
20. Distance-transitive graphs
21. The feasibility of intersection arrays
22. Primitivity and imprimitivity
23. Minimal regular graphs with given girth
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