Cvetkovic D., Doob M., Sachs H. — Spectra of graphs. Theory and application :: Электронная библиотека попечительского совета мехмата МГУ

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Cvetkovic D., Doob M., Sachs H. — Spectra of graphs. Theory and application

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Название: Spectra of graphs. Theory and application

Авторы: Cvetkovic D., Doob M., Sachs H.

Аннотация:

The theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. However, that does not mean that the theory of graph spectra can be reduced to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a theory in its own right.

Язык:

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 368

Добавлена в каталог: 14.03.2005

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Предметный указатель

$A \otimes B$       67
$B^n_{\lambda}(G)$       27
$C_G(\lambda)$       27
$E_{p, q}$       132
$E_{\pi}$       236/237
$F_G(\lambda, \mu)$       28
      65
$G_1\cup G_2$       51 $G_1\times G_2$
$G_1\dot G_2$       52
$G_1\nabla G_2$       54
      44
$P_G(\lambda)$       12
$P_G^{\ast}(\lambda)$       34
$P_G^{\ast}(\lambda_1, \lambda_2, ..., \lambda_s)$       29
$Q_G(\lambda)$       25
$R_G(\lambda)$       26
      27
      23
      26
      26
      27
$S_G(\lambda)$       27
$\alpha(G)$       88
$\beta$ -product      66
$\chi(G)$       15
$\chi(p:\mathcal{R}), \chi(\mathcal{R})$       146
$\eta(G)$       232
$\gamma$ -product      66
$\gamma(G)$       119
$\Gamma, \gamma$       134
$\kappa_R(G)$       260
$\Lambda$ -operator      252 257
$\lambda$ -product      66
$\lambda(F)$       260
$\lambda_R(G)$       260
$\mathbb{E}$ -eigenvalue      123
$\mathbb{E}$ -polynomial      123
$\mathbb{P}\mathbb{G}(3, 2)$       165
$\mathcal{J}$ -sum of graphs      66 76
$\mathcal{M}$ -combination      215 216
$\mathcal{R}$       126; 141
$\mu(G)$       260
$\mu_2(G)$       263
$\mu_R(G)$       260
$\nabla$ -product      54 57 98 99 211
$\sigma$ -electron      229 231
$\sigma$ -factor      111
$\varphi_G(\lambda)$       49
(0, 1, —l)-ineidenee matrix      16 265
(T', T'')-cover      130 133
(—1, 1, 0)-adjacency matrix      26 183 184 195 196 201
8-eage      266
a(G)      265
A-variation with repetitions      212
A.SCHBACHEE, M.      185
Adam, A.      223 224
Adjacency matrix      11*
Adjacent vertices      11*
Admittance, matrix of      27 37—41
Aigner, M.      180 183
Alphabet      131
Amis, A. T.      112
Anderson Jr., W. N.      27 266
Annulene      231
ARC      11*
Ash, R. B.      36
Association scheme      178 193 194 197 198 264
Aufbau — Prinzip      237
Automorphism group      119 121 134—155 161 194 231 269 270
Automorphism group, transitive      136 — 138 153 154
Automorphism of a graph      118*
Babai, L-      134 144 145 153—155
Baghavarao, D.      178
Baker, G-      256
Basis of a NEPS      66*
Bece, A.      36
Beineke, L. W.      170 269
benzene      244
Bhagawandas      103
BIBD      50 165/166 167 173 176 177 185 187 190
BIBD, symmetric      see “Design symmetric”
Biggs, N. L.      7 134 138 194 198
Bingel, G.      97
Binomial coefficient graph of characteristic n      179 180
Biphenyl      244
Blackwell, D.      216
Block design, balanced incomplete      50 165 166 190 197
Block diagonal sum of a matrix      141
Block of a digraph      264
Boiling point      270
Boolean function of graphs      65 67 68—72 203—207
Bose, R. C      103 178 179 183 193 198
Bottema, 0.      259
Bridge      15 242
Brooks theorem      90 102
Brooks, R. L.      38
Brown, W. G.      190
Burnside, W.      148
Butadiene      244
Bvssemaker, F. C      185 197 266 268 269
Cameron, P. J.      177 178
Canonical form of a matrix      141 145
Cardinal product of graphs      66
Cartesian product of graphs      66
Catalan’s constant      247
Cauchy’s inequality      19
Cayley formula      217
Cayley graph      138 153 154 155
Cayley — Hamilton theorem      20 81
Chang, L. C      174
Chao, C.-Y.      144
CHARACTER      146
Chebyshev’s polynomial      73 78 218—220
Chelnokov, V. M,      224
Chen, W.K.      36
Chess board      214 245 247 251
Circuit      15*
Circuit, Hamiltonian      113
Circulant matrix      53 153
Clark, F. H.      36 60
Clatworthy, W. H.      195
Clebsch graph      184 185
Cliques, pair of bridged      170 171 186
Coalescence      158 159
Coates, C. L.      36 47
Cocktail-party graph      72 178 178 197 217
Code, error-correcting      75
Code, error-correcting, perfect      131 190
Coding theory      131
Codivisor      125 126 128 150
cof X      264
Coixatz, L.      13 36 78 84 128 156 160 232 256
Coloration, D-feasible      116 121 123 129
Complement of a graph      16*
Complete product      54 57 58
Complex, linear      118
Complexity of a graph      38 49 50 72 225
Component      15*
Component, strong      55
Composition of graphs      71
Configuration, coherent      194
Conjunction      66
Connection from i to j      47
Connectivity, algebraic      265
Connectivity, algebraic, edge-; vertex-      265 269
Connor, W. S.      195
Cook, C. R.      183
Coreljic, S.      268 269
Coulson — Bushbrooke pairing theorem      232
Coulson, C. A.      36 87 232

Coulson’s bond-order matrix      238
Courant-Weyl inequalities      51 93
Cover, unbranched      118
CP(k)      177
Cube (graph)      225 266 269
Cube, rc-dimensional      178 179 186
Cutpoint      15* Cut set
Cvetkovic, D. M.      8 36 44 46 50 56 57 62—64 68 69 71 77 88 92 101 102 113 131 132 140 175 180 182 186 187 204 206—209 212 213 224 234—236 242—244 258 259 266 269
CYCLE      15*
d(F)      260
d-girth      81
Degree      14*
Degree matrix      16*
Delsahte, P.      183
Dembowski, P.      178
Density matrix      238
Desargues’ graph      266
Design, symmetric      166 167 176 185 187 190 227
Desoer, C. A.      36
Dewar, M. S. J.      241 259
diam (F)      260
Diameter      15 88 162—165 178 179 186 187 192—194 198 269
Digraph      11*
Digraph with weighted adjacencies      35 41 47
Dimer      245—251
Direct sum      64 57 158 162 163 167 186 195 211 219 262
Direct sum of matrices      141*
Dismantling of a graph      234
Distance      15*
Distance, matrix      268 264
Distance, polynomial      263 264 271
Divisor (front, rear)      116—133 149—152 190 198 257
Divisor (front, rear), generalized      118
Divisor (front, rear), proper      117
Djokovic, D. 2.      224
dodecahedron      225 269
Donath, W. E.      114
Doob, M.      8 69 78 107 162 163 165 169 175 176 185—187 223 260 261
Double-m-property      132
Dynamic mean of the valencies      46 217
EDGE      11*
Edge, directed      11*
Edge, multiple      11*
Eigenvalue, simple      18 135—140 162 166 204 270
Eigenvalue, simple, of a graph      12*
Eigenvector of a graph      12*
Elspas, B.      153 167 224
Erdos, P.      191
ethylene      244
Eulers theorem      243
Extended p-sum of graphs      66
Face      242
Factor, (= 1-factor)      239—246 249 251 258 259
Factor, generalized      111
Factor, linear      15 34 35 37 129
Factor, quadratic      129
Factor, regular of degree a      15 107 224 239
Feit, W.      193
Feobenius, F. G.      18
Fibonacci numbers      249 250
Fiedler, M.      27 39 265 266
Figure (elementary, basic)      32 87 88 95 96 240 243 244 259
Finck, H.-J.      57 94 98 102 103 113 133 163
Fisher, M. E.      254—256
Forest      16 37 90 258
Friendship theorem      193
Generating function for the number of walks      44 213 251
Geometry, projective      165
Gewirtz, A.      193
Gibbs, R. A.      187
girth      15 81 87 97 190—193 197 266 269
Godsil, C. D.      144 155
Goethals, J. M.      8 115 177 178 183
Graham, R. L.      264
Gramian matrix      199 — 202
Graovac, A.      241
Graph      11*
Graph, $\nabla$ -prime      98 99 100 207 223
Graph, bicomplete      see “Graph complete
Graph, bipartite      15*
Graph, complete      13 16 72 90 113 162—164 185 196 206 207 211 217 221 223 262 264 269
Graph, complete bipartite      16 50 72 133 158 162—165 174 195 197 206 207 211
Graph, complete multipartite (k-partite, k-complete)      16 73 93 114 133 163 164 170 211 223
Graph, connected      15*
Graph, cyclically k-partite      82 83
Graph, directed      11*
Graph, disconnected      15*
Graph, distance-transitive      183 193 194 197 198
Graph, Eulerian      201
Graph, integral      266
Graph, k-colourable      15
Graph, k-degenerate      90
Graph, linear directed      15*
Graph, metrically regular      178 179 183 186 194 264
Graph, partial      14*
Graph, planar      242 245 256 266
Graph, plane      242 243 256
Graph, prime      182
Graph, properly coloured      15
Graph, regular      14*
Graph, schlicht      11*
Graph, self-complementary      97 98 114 269 270
Graph, semiregular      16 31 42 49 62 133 173—175 186 193
Graph, strong      196 203
Graph, strongly connected      15*
Graph, strongly connected, regular      103 115 140 163 174 179 185 190 193—197 203 226 227
Graph, symmetric      138 193—197 203 226 227
Graph, tetrahedral      180 183
Graph, tetrahedral, totally disconnected      16 99 113 162 196
Graph, tetrahedral, triangular      170 174 184
Graph, tetrahedral, weakly symmetric      138
Graphs, cospectral      24 125 134 153 155 156—161 163 166 170—179 183—187 197 266 267
Graphs, cospectral, isomorphic      12*
Graphs, cospectral, isospectral      see “Graphs cospectral”
Grohmann, G.      57 98
Group, dihedral      155
Group, dihedral of automorphisms      see “Automorphism group”
Group, dihedral of quaternions      153
Group, dihedral of symmetries of a molecule      146
Group, dihedral, orthogonal      143 144
Group, dihedral, unitary      144 145
Gunthard, Hs. H.      146
Gutman, I.      60 231 234—236 238 241 258 259 267
H(n)      170
Hadamard matrix      176 197
Haemebs, W.      19 115
Hakimi, S. L.      112
Hall, K. M.      115
Hamiltonian (operator)      228
Hamming distance      131
Harary, F.      11 36 44 46 112 187 266
Haynsworth, E. V.      20
Heawood’s graph      225
Heilbronner, E.      36 59 128 146 259
Hestbnes, M. D.      197
Heydemann, M. C.      187
Higman, D. G.      193—195 200
Hoffman — Singleton graph      165 197
Hoffman, A. J.      7 8 47 78 79 83 90—93 95 112—115 157 158 160 165 168 170 171 174—176 186 188 260—264
Holt, D.      138
Hosoya, H.      36 264
Howes, L.      92 93 113 262
Huckel matrix      231
Huckel theory      228—238 270
Huckel, E.      13 228 230 231
HUTSCHENREUTHER, H.      38 39
Hydrocarbon, acyclic      244
Hydrocarbon, acyclic, alternant      231 232
Hydrocarbon, acyclic, benzenoid      239 244
Hydrocarbon, acyclic, cata-fuzed      244

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