Aldous J.M., Wilson R. — Graphs and Applications: An Introductory Approach :: Электронная библиотека попечительского совета мехмата МГУ

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Aldous J.M., Wilson R. — Graphs and Applications: An Introductory Approach

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Название: Graphs and Applications: An Introductory Approach

Авторы: Aldous J.M., Wilson R.

Аннотация:

Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use. An important part of learning graph theory is problem solving; for this reason large numbers of examples, problems (with full solutions) and exercises (without solutions) are included.
Accompanying the book is a CD-ROM comprising a Graphs Database, containing all the simple unlabelled graphs with up to seven vertices, and a Graphs Editor that enables students to construct and manipulate graphs. Both the Database and Editor are simple to use and allow students to investigate graphs with ease. Computing Notes and suggested activities are provided.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 444

Добавлена в каталог: 11.04.2008

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Предметный указатель

      45 72
, chromatic index of      310
$deg \upsilon$       35
$indeg \upsilon$       92
      253 261 262
      45 72 281 310
, chromatic index of      310
, chromatic number of      281
, connectivity of      223
, lower bound for thickness of      323
$K_{3, 3}$       245 254 261 262
$K_{r, s}$       48
$K_{r, s}$ , lower bound for thickness of      323
      45
      335
$outdeg \upsilon$       92
      50
      50 81
$\chi(G)$       279
$\chi(G)$ , lower bound for      281 284
$\chi(G)$ , upper bounds for      281 282 284
$\chi^\prime(G)$       304
$\chi^\prime(G)$ , lower bound for      306 309
$\chi^\prime(G)$ , upper bounds for      306 307 308 309
$\kappa(G)$       222
$\lambda(G)$       219
A(d)      115
a(G)      113
Adjacency matrix      113 115
Adjacency matrix associated with Markov chain      131
Adjacent      27 86
Algorithm      22
Algorithm, edge colouring      313
Algorithm, efficient      22 334 338
Algorithm, exhaustion      14
Algorithm, exponential-time      338 339
Algorithm, Fleury's      203 335
Algorithm, greedy      184
Algorithm, heuristic      24
Algorithm, Kruskal's      184 185
Algorithm, planarity testing      256
Algorithm, polynomial-time      338 339
Algorithm, Prim's      188 189 337 338
Algorithm, shortest path      204 211 338
Algorithm, spanning tree      145 335
Algorithm, vertex colouring      288
Alkane      3 23 175 176 180
Appel, K.      295
ARC      16 85
Arc-disjoint st-paths      231
Archaeology      126
Associated adjacency matrix      131
Associated digraph      131
Balanced signed graph      54 55
Balanced situation      54
Bay      152
Bay(i,j)      153
Benzer's Problem      128
Benzer, S.      128
Bicentral tree      179
Bicentre      179
Binary tree      147 171
Binary word      80
Bipartite graph      6 12 47 55 155
Bipartite graph, complete      48
Bipartite graph, examples      48—50
Blocked call      236
Boruvka, O.      184
Brace      10 152
Braced rectangular framework      10 152
Bracing      152
Bracing, minimum      159
Branching tree      147
Bridge      41
Brook's Theorem      282
Brooks, L.      282
Building-up method for spanning tree      145 335
Bus route problems      324 325 327
Capacity      18
Carbon graph      175
Cayley's theorem      165 170
Cayley, A.      139 178 180 295
Central tree      179
Centre      179
Chemistry      3 174
Chinese postman problem      212 337
Chromatic index      304
Chromatic number      279 334
Circumference of graph      58
Classification of problems      20 332 339
Closed trail      42 95
Closed walk      42 95
Colouring planar graphs      284
Colouring problems      292
Column of rectangular framework      12 153
Combinatorial explosion      15 33 164
communication links      296
Compatible edges      257
Competition graph      100
Complement of simple graph      58
Complete bipartite graph      48
Complete graph      45
Component      41
Computer science      149
Conceptual tree      140
Connected digraph      96
Connected graph      41
Connectivity      222 223
Construction problem      20 21 334
Contraction of graph      262
CONVERSE      352
Convex polyhedron      269
Convex polyhedron, dual      273
Cook, S.      342
Counter-example      348
Counting alkanes      23 175 180
Counting binary trees      171
Counting chemical trees      174
Counting graphs      32 33 336
Counting labelled digraphs      336
Counting labelled graphs      32 33 335
Counting labelled trees      164 336
Counting problem      22
Counting trees      163
Counting unlabelled graphs      33 336
Counting unlabelled trees      164 336
Crum Brown, A.      180
cube      46 270 272
Cube graph      46 50 81
Cut vertex      222
Cutset      220
Cutting-down method for spanning tree      145 335
CYCLE      42 95
Cycle graph      45
Cycle method for planarity testing      256
Cycle, feedback      102
Cycle, Hamiltonian      63 97
Cycle, longest/shortest      58
De Morgan, A.      295
Decision problem      339
Decision problem, graph isomorphism      340
Decision problem, travelling salesman      339
Decomposition of graph, edge      317
Decomposition of graph, vertex      292
deg f      249
Degree of face of plane drawing      249
Degree of face of polyhedron      271
Degree of vertex of graph      35
Degree sequence      36
Deterministic computer      340

Diagram-tracing puzzles      76
Digraph      16 85
Digraph, associated with Markov chain      131
Digraph, connected      96
Digraph, disconnected      96
Digraph, Eulerian      97
Digraph, Hamilitonian      97
Digraph, signed      101
Digraph, simple      85
Digraph, strongly connected      96 119
Digraph, unlabelled      89
Dirac's theorem      74
Direct proof      349
Directed graph      16
Disconnected digraph      96
Disconnected graph      41
dodecahedron      46 270 272
Dominating number      297
Dominating set      297 338
Dominating set problem      338 345
Dominating set, minimum      297 338
Domination problems      296
Dominoes      75
Dual of connected planar graph      264
Dual of convex polyhedron      273
Duality      264
Ecology      99
EDGE      6 26
Edge colouring      303
Edge colouring, algorithm      313
Edge connectivity      218 219
Edge decomposition      317
Edge decomposition into matchings      318
Edge decomposition into planar subgraphs      321
Edge decomposition into spanning subgraphs      324
Edge decomposition into spanning trees      327
Edge-disjoint st-paths      226
Edge-dominating set problem      338
Edmonds, J.      337
Efficient algorithm      22 334 338
Enumeration problem      20 22 335
Euler's formula for planar graphs      251
Euler's polyhedron formula      270
Euler, L.      38 65 271
Eulerian digraph      97
Eulerian graph      63 64 317
Eulerian trail      63 97
Exhaustion method      14
Existence problem      20 333
Explorer's problem      62
Exponential-time algorithm      338 339
Face of plane drawing      248
Face of polyhedron      269
Face-regular graph      249
Family tree      140
Feedback cycle      102
Five colour theorem for planar graphs      285
Fleury's algorithm      203 335
Flow      18
Food web      100
Ford, L.R.      235
Forest      161
Four colour problem      295 333
Four colour theorem for planar graphs      288
Four cubes problem      51
Four cubes problem, generalized      344
Framework      10
Fulkerson, D.R.      235
Games of strategy      148
Gas, water and electricity problem      4 6 28 242
Genetics      128
Girth of graph      58
Goldbach, C.      271
Golf course layout      243
Grammatical tree      148
Graph      6 26
Graph decomposition, edge      317
Graph decomposition, vertex      292
Graph isomorphism decision problem      340
Graph, balanced signed      54
Graph, bipartite      6 47 48—50 55 155
Graph, carbon      175
Graph, circumference of      58
Graph, competition      100
Graph, complement of      58
Graph, complete      45
Graph, complete bipartite      48
Graph, connected      41
Graph, contraction of      262
Graph, cube      50 81
Graph, cycle      45
Graph, decomposition of      292 317
Graph, directed      16
Graph, disconnected      41
Graph, dual      264
Graph, edge decomposition of      317
Graph, Eulerian      63
Graph, face-regular      249
Graph, girth of      58
Graph, Hamiltonian      63
Graph, interval      127
Graph, k-colourable      279
Graph, k-cube      50 81
Graph, k-edge colourable      304
Graph, labelled      32
Graph, line      58
Graph, niche overlap      100
Graph, non-planar      244
Graph, null      45
Graph, orientable      109
Graph, path      50
Graph, Petersen      47 144 255 262
Graph, planar      244
Graph, Platonic      46
Graph, r-regular      43
Graph, regular      43 45—47
Graph, semi-Eulerian      67
Graph, semi-Hamiltonian      74
Graph, signed      54
Graph, simple      26
Graph, subdivision of      260
Graph, thickness of      322
Graph, tour      296
Graph, underlying      92
Graph, unlabelled      31
Graph, vertex decomposition of      292
Graph, weighted      13
Gray code      81
Greedy algorithm      184
Greedy algorithm, edge colouring      313
Greedy algorithm, Kruskal's      184 185
Greedy algorithm, Prim's      188 189 338
Greedy algorithm, vertex colouring      288
Guthrie, F.      295
Haken, W.      295
Hamilton, W.R.      71
Hamiltonian cycle      63 97 344
Hamiltonian cycle, minimum weight      191
Hamiltonian digraph      97
Hamiltonian graph      63 71
Hampton Court maze      8
Handshaking dilemma      94
Handshaking lemma for digraphs      94
Handshaking lemma for graphs      37 44
Handshaking lemma for planar graphs      249
Handshaking lemma for polyhedra      271
Heuristic algorithm      24
Heuristic algorithm for edge colouring      313
Heuristic algorithm for planarity testing      256
Heuristic algorithm for travelling salesman problem      192 196

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