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| Brualdi R.A., Ryser H.J. — Combinatorial Matrix Theory |
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| Предметный указатель |
Network 164
Network matrix 32 33
Network, capacity-constrained 164
Network, supply-demand 169
Newton's formula 334
Nilpotent index 335—337
Nilpotent matrix 335—343
No-parallels postulate 280
Nonzero diagonal 112 136
NP 245—248
NP-complete problem 246—247 268
Nullity 336 338 340
Orthogonal latin squares (MOLS) 269—284
Orthogonal mate 271 272
P 245—248
Pair wise balanced design 278—283
Paley graph 151
Parallel class of lines 277
Parallel lines 279
Parallel postulate 278
Partial transposition 142
Partial transversal 251—252 254—258
Partition 192 336
Partition closure 196
Partly decomposable matrix 112
Path 54
Path-number sequence 337 338 339—340
Perfect matching 247 251 258 318—319 321—322
Perfect matching, random algorithm for 322
Permanent 8 15 18 68 117 136 198—249 292 295 313 314—316
Permanent, conversion of 236—245
Permanent, evaluation of 199—200 235—248
Permanent, inequalities for 214—234
Permanental minor 203—204
Permutation digraph 292
Permutation matrix 1
Permutation matrix, 3-dimensional 252—253
Permutation matrix, Frobenius normal form 60
Permutation, sign of 291
Permutation, simultaneous 25
Petersen graph 37 148 154
Petersen graph, complexity of 43
Petrie matrix 19
Pfaffian 318—323
Playfair's axiom 278
Poincare's theorem 31
POINTS 270 278
Polynomial algorithm 245—248
Polynomial digraph 157—163
Polynomial identity 327—334
Primitive matrix 70 73—74 78—87 117 158
Primitive matrix, exponent of 74 78—87
Problem of the 36 officers 271—272
Projective plane 15—17 20—21 280—281 282 283
Projective plane, order of 281
Quasigroup 251
Reduced adjacency matrix 107 178
Reducible matrix 55
Regular graph 145—147 155
Rook numbers 205—206
Rook polynomial 205—206
Rook vector 205—206 206—208
Row-linear set 139
Ryser's permanent formula 199—200
Satisfiability problem (SAT) 246—247
Search 97
SearchComp 101
Set difference matrix, formal 305 309
set differences 307
Set intersections 11
Sets of imprimitivity 70
Sharp P-complete problem 247
Sign of number 238
Sign pattern 238
Sign-nonsingular matrix 238—244 248
Sign-nonsingular matrix, maximal 248
Singularity 321—322
| Sink 164
Skew-symmetric matrix 317 319—320
Smith's matrix 21—22
Smith's theorem 21—22
Source 164
Spanning arborescence 324—327
Spanning arborescence, root of 324
Spanning directed tree 324
Spectrum 26 27
Splitting of arc 243—244
Splitting of vertex 243—244
Standard polynomial 317 329 331—334
Star 28
Star, algebraic connectivity 43
Star, spectrum 28
Stirling number, second kind 208
Strong components 54
Strongly connected digraph 157
Strongly regular graph 148—155
Strongly regular graph, complement 149
Strongly regular graph, eigenvalues 150
Strongly stable hypergraph 137
Strongly stable set 137 138—139 143
Subdivision 643—644
Subpermutation matrix 49—51 125 128 135 184—188 188—196 267—268
Supply 169
Symbolic direct product 274
Symmetric matrix 129—130
Symmetric matrix, existence theorems for 179—184
Symmetric matrix, exponent 80 85
Symmetric matrix, index of imprimitivity 78
System of distinct represenatives (SDR) 7 10 201 227 247
System of distinct represenatives (SDR), Hall's theorem 7
Term rank 7 10 110 111 114 189 214 294 303 338
Total support matrix 115 116 232
Totally unimodular matrix 31—34
Touchard's formula 205
Tournament matrix 54 55 109
Tournament matrix, Frobenius normal form of 60
Trail 25
Trail, directed 54
Transversal 227 251—252 253 258 268 281
Transversal, common 227
Transversal, weak 255—256
TREE 32 37 38 39 230 343
Tree, adjacency matrix of 184
Tree, algebraic connectivity 43
Tree, directed 65—66 96—99
Tree, incidence matrix of 37
Tree, oriented 32
Tree, spanning 38 97
Triangular graph 152
Tridiagonal matrix 393
Trivial trace identities 329
Tutte's theorem 45—48 320—322
Valency 24
Valiant's hypothesis 247—248
Vector 11
Vector, column sum vector 172
Vector, conjugate 175
Vector, diagonally restricted 177—178
Vector, majorized by 11 175
Vector, monotone 172
Vector, row sum vector 172
Vertical line 277
Vizing's theorem 49—51 125
Walk 25 26
Walk, closed 25
Walk, directed 54
Walk, endpoints 25
Walk, open 25
Wedge product 322—323
Weighted digraph 243 291—292
Weighted digraph, weight of arc 325 335
Weighted digraph, weight of digraph 325
Weighted digraph, weight of directed cycle 291—292
width 337 338
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