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Brualdi R.A., Ryser H.J. Ч Combinatorial Matrix Theory
Brualdi R.A., Ryser H.J. Ч Combinatorial Matrix Theory



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Ќазвание: Combinatorial Matrix Theory

јвторы: Brualdi R.A., Ryser H.J.

јннотаци€:

The book deals with the many connections between matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorical properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix and Latin squares. The book ends by considering algebraic characterizations of combinatorical properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jorda Canonical Form.


язык: en

–убрика: ћатематика/

—ери€: —делано в холле

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1991

 оличество страниц: 380

ƒобавлена в каталог: 16.05.2011

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
${e}_{n}$      145
${l}_{2}$-norm      213Ч214
Acyclic digraph      335 340 343
Adjacency matrix      25 48Ч52 53 179 317
Adjacency matrix, formal      317Ч323 324
Adjacency matrix, isomorphic      157
Adjacency matrix, regular      157 160
Adjacency matrix, tree      343
Adjugate      301
Admittance matrix      30 see
Affine plane      278Ч80
Affine plane, order of      280
Amitsur Ч Levitzki theorem      331Ч334
ARC      53
Arc, back arc      98
Arc, capacity of      164
Arc, cross arc      98
Arc, dominant      89Ч90
Arc, forest arc      98
Arc, forward arc      98
Arc, weight of      291Ч292
Bipartite graph      44 107Ч144 178 317
Bipartite graph, adjacency matrix of      44
Bipartite graph, bipartition of      44 107
Bipartite graph, complete      108 135 147 148 162:
Bipartite graph, complete, line graph of      153
Bipartite graph, elementary      124
Birkhoffs theorem      9
BLOCKS      278
Branch      62 63
Cayley table      250Ч251 254Ч255 258 262 268 271
Cayley Ч Hamilton theorem      327Ч329 333
Chain      25 210
Chain, directed      54
Chain, length of      210
Chain, weight of      211 212
Characteristic polynomial      26 28 36 76Ч77 88 328Ч329
Chromatic index      51
Circuit      54
Circulant matrix      158Ч162 233
Circulation      168Ч169
Co-term rank      125Ч126 134
Cocktail party graph      36Ч37
Column-linear set      139
Complete digraph      291
Complete graph      23 26 39 318
Complete graph, line graph of      152
Complete graph, spectrum of      28
Complete mapping      251
Completely reducible matrix      76
Complexity (of a graph)      38Ч40 324
composition      191 196
Conference graph      151 155
Conference matrix      154
Configuration      3 20 293 306 307Ч308
Configuration, complementary      305
Configuration, dual      4 12
Configuration, isomorphic      4
Conjugate partition      193 340
Connectivity, algebraic      40Ч53
Connectivity, edge      41
Connectivity, vertex      41
Contraction      62 242
Convex closure      193Ч195
Convex sequence      192 340
Cospectral graphs      26Ч27 155
Cover (of digraph)      134
Covering sequence      190Ч196
Cut      166
Cut, capacity of      166
CYCLE      25
Cycle graph      28
Cycle hypergraph      144
Cycle, directed      54
Cyclic components      71
Cyclic components, computation of      103Ч105
Cyclic matrix      77
Decision problem      245Ч248
Decision problem, polynomial reducible      246
Decision problem, size of      245
Decomposition      251
Decomposition theorems      108 125Ч136 184Ч188
Degree of vertex      24
demand      169
Depth-first number      97
Depth-first search      97
Derangement number Dk      17 222Ч223 233
Derangements      201Ч202 285
Determinant      8 15 16 21Ч22 76 89 90 92 93 94 95 134 209Ч214 235Ч48 291Ч293 294 295 296Ч297 298Ч299 301 309Ч310 311 313Ч314 314Ч316 319 323 325Ч326
Determinantal divisor      337
Diagonal      112
Diagonal structure (hypergraph)      136Ч144
Diagonal structure (hypergraph), isomorphism of      136Ч137
Diagonal structure (hypergraph), partial transposition      142Ч143
Diagonal structure (hypergraph), permutation      140
Diagonal structure (hypergraph), transposition      140
Difference sequence      191 195Ч196 338 339Ч340
Digraph (directed graph)      53 243
Digraph (directed graph), adjacency matrix of      53
Digraph (directed graph), capacity function      164
Digraph (directed graph), characteristic polynomial      88
Digraph (directed graph), condensation      56
Digraph (directed graph), cyclically r-partite      70
Digraph (directed graph), general      53
Digraph (directed graph), girth of      93
Digraph (directed graph), imprimitive      68Ч69
Digraph (directed graph), indegree sequence      173 176
Digraph (directed graph), minimally strong      61Ч68
Digraph (directed graph), out degree sequence      173 176
Digraph (directed graph), primitive      68
Digraph (directed graph), regular      53
Digraph (directed graph), spanning subdigraph      97
Digraph (directed graph), spectrum      88
Digraph (directed graph), splitting of      244
Digraph (directed graph), strongly connected      54 55Ч61
Digraph (directed graph), vertex-weighted      89Ч90
Directed cycle, dominant      90
Directed cycle, weight of      243
Directed forest      96Ч99
Directed forest, spanning      97
Divisor sequence      337Ч338 339Ч340
Doubly stochastic matrix      9 11 117
EDGE      23
Edge coloring      50
Edge, endpoints      23
Eigenvalue inclusion regions      89Ч95
Eigenvalues      16 26 27 76Ч77 88Ч96 130Ч132 145 146
Elementary divisors      337
Elementary similarity      341
Essential column      110
Essential line      110
Essential row      110
Euler $\phi$-function      21Ч22
Euler conjecture      275 282Ч283
Eulerian matrix      31
Eulerian trail      332
Evans conjecture      263Ч267
Even digraph      243Ч244
EXPONENT      78Ч87 83Ч85 117
Exponent, gaps      84
Factor      48
Ferrers matrix      206Ч207 208 217
Flow (network)      164Ч171
Flow (network), supply-demand      169Ч171
Flow (network), value of      165
Forest      178
Friendship theorem      151
Frobenius normal form      58 96Ч102
Frobenius normal form, computation of      96Ч106
Frobenius Ч Schur index      72 81
Fully indecomposable components      115 140Ч141 297
Fully indecomposable matrix      110Ч118 124 228Ч233 296Ч297 299 303
Fully indecomposable matrix, inductive structure      116
Fundamental trace identity      327 329Ч331
Gale Ч Ryser Theorem      176
Galois affine plane      279 280
General digraph      53
Generalized matrix function      295
Generic matrix      294Ч297
Generic nilpotent matrix      335Ч343
Generic skew-symmetric matric      317
Gersgorin's theorem      88
Graph (general)      23 24
Graph (general), adjacent      23
Graph (general), complement      23
Graph (general), complete      23 26
Graph (general), complete multipartite      147 155
Graph (general), connected      27
Graph (general), connected components      27
Graph (general), cospectral      26Ч27 155
Graph (general), cubic      24 37
Graph (general), decomposition of      108 109
Graph (general), degree sequence      179 183
Graph (general), diameter      27
Graph (general), disconnected      27
Graph (general), distance      27
Graph (general), edge      23
Graph (general), induced      23
Graph (general), isolated      23
Graph (general), isomorphic      23 25 26
Graph (general), multiplicity of      24
Graph (general), order      23
Graph (general), regular      24 37 43
Graph (general), simple      23
Graph (general), spanning      23 30
Graph (general), spectrum of      28
Graph (general), subgraph      23
Graph (general), vertices      23
Hadamard product      294 317
Hadamard's determinant inequality      214
Hall's theorem      299Ч301
Hamilton cycle problem      245Ч246 247
Helly type theorem      19Ч20
Hoffman polynomial      147 157 162
Hoffman Ч Singleton graph      154
Horizontal line      277
Imprimitive matrix      70
Incidence matrix      3 29 35 230 304 306
Incidence matrix, formal      293Ч303
Incidence matrix, oriented      29 38
Incidence matrix, weighted      210Ч214
INDEX      103Ч105
Index of imprimitivity      68Ч78
Index of imprimitivity, computation of      103Ч105
Integer sequences      191Ч195
Intersection matrix      11Ч12
Intersection matrix, formal      304Ч310
Intersection matrix, symmetric      305 306 309
Invariant factors      337
Irreducible components      58
Irreducible components, computation of      96Ч106
Irreducible matrix      55Ч61 113 145 297Ч300
Irreducible matrix, inductive structure      67Ч68
Jacobi's identity      321Ч322 301
Join      192
Jordan block      336 340Ч343
Jordan canonical form      335Ч337 340Ч343
Jordan partition      336 338 339Ч340 343
Jordan partition, length of      336
K-decomposition      187
k-path      336Ч337 338
k-path number      336Ч337
k-subset      203
Koenig's Theorem      6 9 44 47 125 128 196 300 301Ч303
Laplacian matrix      30 38 41 325
Laplacian matrix, formal      324Ч327
Latin rectangle      250Ч253
Latin rectangle, completion of      260Ч262 68
Latin square      250Ч290
Latin square, completion of      259Ч262
Latin square, embedding of      262Ч263
Latin square, enlargement of      265Ч267
Latin square, equivalent      253
Latin square, horizontal line of      270
Latin square, idempotent      281Ч283 283Ч284
Latin square, latin line of      270 277
Latin square, mutually orthogonal      272Ч275 286Ч287
Latin square, normalized      250
Latin square, number of      284Ч285
Latin square, partial      259Ч269
Latin square, partitioning of      262Ч263
Latin square, self-orthogonal      287Ч288 289
Latin square, symmetric      251 268 269 283
Latin square, vertical line of      270
Lattice graph      153
Line      1 252 277 278
Line cover      6 110Ч112
Line graph      35Ч37
Line graph, spectrum of      35
Linear set      139
Linearizable set      143 144
Lowlink      100Ч101
MacMahon's master theorem      310Ч316
MacNeish's conjecture      275 282Ч283
Majorization      175
Matching      44Ч52 112 189
Matching sequence      189Ч196
Matching, in digraph      134
Matching, perfect      48
Matrix      1
Matrix, back diagonal of      263
Matrix, column sum vector      172
Matrix, complement of      3 12
Matrix, cover of      6
Matrix, cyclic      70
Matrix, cyclic components      71
Matrix, diagonally dominant      89
Matrix, elementwise product      236
Matrix, existence theorems for      172Ч184
Matrix, line of      1
Matrix, number of l's      123
Matrix, permutation      1
Matrix, principal      17
Matrix, proper cover of      6
Matrix, row sum vector      172
Matrix, submatrix of      17
Matrix, sum of elements of      185
Matrix, triangle of      18
Matrix, upper triangular      338Ч339
Matrix-tree theorem      325Ч326
Matroid, regular      31Ч34
Matroid, unimodular      31Ч34
Max flow-mincut theorem      166Ч168
Meet      192
Menage numbers      202Ч203 204Ч205 233 234 285
Minimax theorem      6
Mixed matrix      303
Moore graph      153
Moore graph, generalized      154
Multicolored graph      131Ч132
Multiedge      24
Multigraph      23
n-set      3
Nearly decomposable matrix      118Ч124 228
Nearly decomposable matrix, inductive structure      120Ч121
Nearly decomposable matrix, number of l's of      122
Nearly reducible matrix      61Ч68 118 124
Nearly reducible matrix, inductive structure      64
Nearly reducible matrix, number of, 1's of      66
Net      277Ч280
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