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Godsil C., Royle G. — Algebraic Graph Theory
Godsil C., Royle G. — Algebraic Graph Theory

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Название: Algebraic Graph Theory

Авторы: Godsil C., Royle G.

Аннотация:

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. The authors take an inclusive view of the subject, and present a wide range of topics. These range from standard classics, such as the characterization of line graphs by eigenvalues, to more unusual areas such as geometric embeddings of graphs and the study of graph homomorphisms. The authors' goal has been to present each topic in a self-contained fashion, presenting the main tools and ideas, with an emphasis on their use in understanding concrete examples. A substantial proportion of the book covers topics that have not appeared in book form before, and as such it provides an accessible introduction to the research literature and to important open questions in modern algebraic graph 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. His main research interests lie in the interactions between algebra and combinatorics, in particular the application of algebraic techniques to graphs, designs and codes. He has published more than 70 papers in these areas, is a founding editor of "The Journal of Algebraic Combinatorics" and is the author of the book "Algebraic Combinatorics". Gordon Royle teaches in the Department of Computer Science & Software Engineering at the University of Western Australia. His main research interests lie in the application of computers to combinatorial problems, in particular the cataloguing, enumeration and investigation of graphs, designs and finite geometries. He has published more than 30 papers in graph theory, design theory and finite geometry.


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 232

Добавлена в каталог: 29.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\chi$-critical      105
1-Factor      43
1-factorization      73
2-cell embedding      404
5-prism      7
Achiral      376
action      19
Acyclic graph      4
Acyclic orientation      321
Adjacency matrix      163
Adjacent      1
Adjoint      108
Adjugate      283
Algebraic connectivity      305
Alternating cycle      418
Alternating knot      381
Arborescence      303
ARC      35
Arc of a link diagram      377
Arc, in a graph      2
arc, regular      63
Arc, s-arc      59
Arc, s-arc transitive      59
Arc, transitive      35
asymmetric      22
atom      40
Automorphism group of a graph      4
Automorphism of a graph      4
Automorphism of a group      48
Balanced representation      285
Barycentric representation      294
Basis of a matroid      343
Bent eulerian partition      397
Bicycle      332
Bicycle space      333
Bicycle space of a code      351
Bicycle-type      335 351
Binary matroid      349
Bipartite graph      6
Bisection width      293
Block graph      97
Block of a design      94
Block of a graph      347
Block of imprimitivity      27
BOND      308
Bond matroid      345
Bridge      37
Cartesian product      154
Cayley graph      34
Chang graphs      259
Characteristic matrix      196
Characteristic polynomial      164
Chip firing      321
Chord      311
Chord diagram      405
Chromatic number      7
Chromatic polynomial      354
Circle graph      406
Circuit of a matroid      343
Circulant graph      8
Circular chromatic number      157
Clebsch graph      226
CLIQUE      3
Closed left-right walk      400
Closed walk      165 395
Cofactor      283
Colin de Verdiere number      305
Collinear      78
Coloop      346
Colour class      7
Colouring      6
Colouring of a link diagram      378
Comparability graph      143
Complement      5
Complete bipartite graph      12
Complete graph      2
Completely regular      196
Component of a graph      4
Component of a link      374
concurrent      78
Conductance      292
Conference graph      222
Conjugacy class      21
conjugate      21
Connected component      4
Connected graph      4
Connected matroid      347
Connection set of a circulant      8
Connectivity      39
Contraction      346
Core      104
Core of a graph      105
Cospectral      164
Covering graph      115
Covering map      115
Critical      105
Critical group      329
cube      14 33
Cube, k-cube $Q_k$      33
Cubic      5
Cut      308
Cut lattice      317
Cut space      308
Cut-edge      37
Cut-type      335 351
CYCLE      4
Cycle , $C_n$      8
Cycle matroid      343
Cyclic interval graph      145
Decomposable      268
Deletion      346
Deletion-contraction algorithm      349
Dependent set      343
Determinant      317
Diagonal of a product      107
Diagonal, orbital      26
Diameter      16
Diffuse state      325
Direct sum      347
Directed edge      2
Directed graph      2
Disconnected      4
Disjoint union      4
Distance      5
Distance partition      67
Distance regular      68
Distance transitive      66
Dollar game      327
Double occurrence word      404
Dowker code      425
Dual code      348
Dual function      344
Dual graph      14
Dual incidence structure      78
Dual lattice      316
Dual map      416
Dual matroid      345
Duality      79
Ear decomposition      313
EDGE      1
Edge, atom      38
Edge, colouring      65
Edge, connectivity      37
Edge, cutset      37
Edge, transitive      35
Empty graph      2
Endomorphism      8
Endomorphism monoid      8
Energy      285
Equiangular lines      249
Equitable partition      195
Equivalent links      374
Eulerian cycle      396
Eulerian orientation      370
Eulerian partition      396
Eulerian tour      396
Eulerian walk      395
Even double occurrence word      404
Even graph      318
Expander      293
External face      13
Face graph      379
Face of a plane graph      13
Faithful      19
Fano plane      95
Feasibility condition      219
Fibre of a homomorphism      104
Finite graph      2
Firing, chip firing      321
Flag      414
Flat      369
Flip, a double occurrence word      407
Flip, an eulerian tour      397
Flipping the rotor      364
Flow lattice      318
Flow polynomial      370
Flow space      310
Flow-type      335 351
Folding      114
Forest      4
Fractional chromatic number      136
Fractional clique      136
Fractional clique number      136
Fractional colouring      135
Fragment      40
Fullerene      208
G-invariant      20
Gauss code      403
Generalized Laplacian      296
Generalized line graph      266
Generalized polygon      84
Generalized quadrangle      81
Generating set      49
Generator matrix      342
Generously transitive      26
girth      60
Gram matrix      173
Graph      1
Graphic matroid      346
grid      82
Halin graph      25
Hamilton cycle      45
Hamilton path      45
Hamiltonian      45
Head of an edge      167
Heptad      69
Hoffman — Singleton graph      92
Homeomorphism      374
Homomorphically equivalent      104
Homomorpliism      6
Hull of a code      351
Hyperplane      370
Hypohamiltonian      66
icosahedron      127
Imperfect      142
Imprimitive graph      218
Imprimitive group      28
In-valency      29
incidence      78
Incidence graph      78
Incidence matrix of a design      95
Incidence matrix of a graph      165
Incidence matrix of an oriented graph      167
Incidence structure      78
Incident point and line      78
Incident vertex and edge      1
Indecomposable      268
Independent set      343
Independent set of vertices      3
Index of a cover      115
Induced subgraph      3
Infinite face      13
Integral basis      315
Integral lattice      316
Interlace      193
Intersection array      68
Intersection numbers      239
Invariant      170
Irreducible      175
Isometric      16
Isomorphic      1
Isomorphism      2
Isomorphism class      22
Isoperimetric number      292
Isotopy      374
Isotropic      215
Johnson graph      9
Jones polynomial      388
k-connected      39
k-regular      5
Kauffman bracket      384
Kernel of a homomorpliism      104
Kneser graph      9
Knot      374
Krein bound      231
Kronecker product      206
LADDER      131
Laplacian      279
Latin square      69
Lattice      107 315
Laurent polynomial      388
Leapfrog graph      209
Left right cycle      400
Left-right walk      399
Lexicographic product      17 156
Line graph      10
Linear code      342
Linear group      81
Linear matroid      349
Link      374
Link diagram      374
Link invariant      377
Local complement      182
Local eigenvalue      228
Local injection      115
Local isomorphism      115
Loop in a graph      8
Loop in a matroid      344
MAP      415
Map graph      108
Matching      43
Matroid      343
Maximal planar graph      13
Maximal spanning forest      4
Maximum matching      43
Medial graph      398
Minimal asymmetric graph      32
Minimally imperfect      143
Minor      300
Mirror image      375
Moebius ladder      118
Monoid      8
Monotone      341
Moore graph      90
Multiple edge      14
Mutant knots      390
n-colouring graph      155
n-full      192
Neighbour      1
Nodal domain      297
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