000			03231cam a2200349 a 4500
001			4914830
003			CUTN
005			20231114163511.0
008			940610s1993 enk b 000 0 eng d
010			_a 94170202
020			_a9780521458979
035			_a(OCoLC)30411209
040			_aTxHR _cTxHR _dDLC
042			_alccopycat
050	0	4	_aQA166 _b.B53 1993
082	0	0	_a511.5 _220 _bBIG
100	1		_aBiggs, Norman.
245	1	0	_aAlgebraic graph theory / _cNorman Biggs.
250			_a2nd ed.
260			_aCambridge : _bCambridge University Press _c1993.
300			_avi, 205 p. ; _c23 cm.
440		0	_aCambridge mathematical library
504			_aIncludes bibliographical references (p. [191]-201) and index.
505			_a 1. 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		0	_aGraph theory.
856	4	2	_3Publisher description _uhttp://www.loc.gov/catdir/description/cam026/94170202.html
856	4	1	_3Table of contents _uhttp://www.loc.gov/catdir/toc/cam029/94170202.html
906			_a7 _bcbc _ccopycat _d3 _encip _f19 _gy-gencatlg
942			_2ddc _cPROJECT
999			_c40358 _d40358