000			03085nam a22003017a 4500
003			OSt
005			20260610164447.0
008			260610b |||||||| |||| 00| 0 eng d
020			_a1316616916
020			_a9781316616918
041			_aeng
082			_a511.5 BIG-A
100			_aBiggs, Norman. _983676
245			_aAlgebraic graph theory
250			_a2nd
260			_aCambridge : _bCambridge University Press, _c2018.
300			_avii, 205p.
440			_aCambridge Mathematical Library _983677
505			_a1. Introduction to algebraic graph theory Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph 3. Regular graphs and line graphs 4. Cycles and cuts 5. Spanning trees and associated structures 6. The tree-number 7. Determinant expansions 8. Vertex-partitions and the spectrum Part II. Colouring Problems: 9. The chromatic polynomial 10. Subgraph expansions 11. The multiplicative expansion 12. The induced subgraph expansion 13. The Tutte polynomial 14. Chromatic polynomials and spanning trees Part III. Symmetry and Regularity: 15. Automorphisms of graphs 16. Vertex-transitive graphs 17. Symmetric graphs 18. Symmetric graphs of degree three 19. The covering graph construction 20. Distance-transitive graphs 21. Feasibility of intersection arrays 22. Imprimitivity 23. Minimal regular graphs with given girth References Index.
520			_aThis is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he 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. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.
650			_aGraph theory _983826
650			_aAlgebra _983827
650			_aAlgebraic graph theory. _983828
856			_uhttps://www.cambridge.org/in/universitypress/subjects/mathematics/discrete-mathematics-information-theory-and-coding/algebraic-graph-theory-2nd-edition?format=PB&isbn=9780521458979#contents
856			_uhttps://assets.cambridge.org/97805214/58979/toc/9780521458979_TOC.pdf
942			_cBK
999			_c200713 _d200713