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Cvetkovic D., Rowlinson P., Simic S. — Eigenspaces of Graphs
Cvetkovic D., Rowlinson P., Simic S. — Eigenspaces of Graphs



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Название: Eigenspaces of Graphs

Авторы: Cvetkovic D., Rowlinson P., Simic S.

Аннотация:

Graph theory is an important branch of contemporary combinatorial mathematics. By describing recent results in algebraic graph theory and demonstrating how linear algebra can be used to tackle graph-theoretical problems, the authors provide new techniques for specialists in graph theory. The book explains how the spectral theory of finite graphs can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labeling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. Current research on these topics is part of a wider effort to forge closer links between algebra and combinatorics. Problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 258

Добавлена в каталог: 08.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
2-design      14
Algorithm, deletion-contraction      108
Algorithm, Edmonds'      205
Algorithm, reconstruction      112
Alphabet      41
angles      21 75 234
Angles, main      76
Angles, partial      95
Aufbau principle      227
Automorphism      43
Block design      14
Block, internal      117
Block, terminal      117
Block, trivial      117
Bond length      227
Bond order      227
Boolean operations      30
Bound, absolute      214
Bound, Chernoff      50
Branch      105
Branch, internal      120
Branch, terminal      120
Carbon skeleton      226
Cauchy's inequalities      37
Centre      120
Characteristic polynomial      1
Characteristic vector      48
Characterizations, spectral      11
Chess board      27 33
Coalescence      4 89
Code, canonical      192
Code, perfect      41
Coefficient, perturbation      137
Colouring      38
Colouring, regular      38
Condition bridge      123
Condition edge      125
Connectivity, algebraic      54
Connectivity, edge      54
Connectivity, vertex      54
Digraph, Koenig      4 198
Direction, main      97
Divisor      38
Dominating set      171
Dominating set, minimal      171
EA-reconstructible invariant      83
EA-reconstructible property      83
Edge, subdivided      57
Eigenspace      2
Eigenvalue, largest      3
Eigenvalue, main      25
Eigenvalue, second largest      223
Eigenvalue, simple      45
Eigenvalue, smallest      16
Eigenvalues      1
Eigenvalues, conjugate      187
Eigenvalues, corresponding      46
Eigenvector      2
Eigenvector, non-negative      23
Eigenvector, partial      184
Eigenvector, principal      3
Electron charge      77 227
Exit-value      184
Factor      48
Forests, cospectral      9
Form, biquadratic      60
Formula, Coates      122
Formula, Heilbronner      135
Formula, Jacobi      122
Formula, Schwenk      122
Function spaces      27
Function, even      35
Function, odd      35
Fuzzy image      126
Graph ordering by spectral moments      109
Graph ordering by spectrum      109
Graph ordering, canonical      192
Graph, bicyclic      4
Graph, bicyclic, central part of      115
Graph, bicyclic, Hamiltonian      59
Graph, bicyclic, tail of      115
Graph, bipartite      15
Graph, Chang      5
Graph, cocktail party      4
Graph, complete, k-partite      4
Graph, cubic      78
Graph, cubic lattice      19
Graph, cubic, path-like      119
Graph, cubic, tree-like      117
Graph, Hamiltonian      72
Graph, Hamiltonian, tricyclic      61
Graph, icosahedral      136 142
Graph, Latin square type      230
Graph, molecular      226
Graph, outerplanar, maximal      50
Graph, partial      95
Graph, perturbed      132
Graph, quasi-bridge      123
Graph, random      50
Graph, recognition      52
Graph, regular      15 23
Graph, Schlaefli      6
Graph, semi-regular bipartite      13
Graph, strongly regular      77 211
Graph, tetrahedral      20
Graph, tricyclic      4
Graph, unicyclic      4 109
Graph, walk-regular      79
Graph, weight-generated      196
Graph, weight-generated, modified      196
Graph, weighted      195
Graph, weighted, canonical ordering      197
Graphs, cospectral      6
Graphs, cospectral, connected      8
Graphs, cospectral, regular      9
Graphs, endospectral      10
Graphs, isospectral      6
Graphs, subspectral      11
Graphs, switching-equivalent      5
Group automorphism      43
Hamming distance      41
Heuristic Kernighan — Lin      211
Hueckel's theory      226
Immanant      10
INDEX      3
Interlacing theorem      37
Intermediate eigenvalue problems      143
Invariant, complete      20
Involution      45
J-sum of graphs      30
Join      4
King      27
Knight      32
Kronecker product      31
Length walk      24
Length word      41
Limb      105 120
Line graph      5
Line graph, generalized      5
Lloyd's Theorem      41
Location-dominating set      172
Matching      4
Matching, perfect      4 198
Matrix, adjacency      1
Matrix, adjacency, stepwise      60
Matrix, admittance      6
Matrix, angle      76
Matrix, bond-order      227
Matrix, density      227
Matrix, eigenvector      156
Matrix, Hadamard      14
Matrix, hermitian      37
Matrix, imprimitive      233
Matrix, incidence      6
Matrix, irreducible      23
Matrix, Laplacian      6
Matrix, perturbed      136
Matrix, primitive      233
Matrix, reducible      232
Matrix, Seidel      5
Matroid theory      204
Measure of irregularity      74
Neighbourhood, closed      158
Neighbourhood, open      158
NEPS      30 91
NEPS, coincidence-free      93
Number of pentagons      82
Number of quadrangles      82
Number of triangles      81 82
Number, chromatic      101
Number, domination      172
Number, isoperimetric      55
Number, location-domination      172
Optimization, combinatorial      193
Orbital, atomic      226
Orbital, molecular      226
p-sum of graphs      30
Partition, admissible      95
Partition, equitable      38
Partition, feasible      151
Partition, natural      225
Partition, polynomial      153 183
Partition, star      21 151
Partition, star, line      189
Partition, walk      38
Path, augmenting      201
Path, internal      57
Pendant edge      87 141
Permanent      10
Perturbations, algebraic theory      142
Perturbations, analytical theory      136
Ping      6
Plane, affine      14
Plane, protective      14
Polynomial, characteristic      1
Polynomial, characteristic, generic      99
Polynomial, Chebyshev      62
Polynomial, graph      15
Problem, graph isomorphism      6
Problem, graph reconstruction      127
Problem, matching      198
Problem, matroid intersection      204
Problem, maximal clique      208
Product of graphs      30
Product, generalized direct      30
Pseudo-net-graph      230
Quasi-bridge      124
Quasi-graph      125
Rayleigh quotient      49 193
Reconstruction Conjecture      126
Reconstruction Lemma      111
Reconstruction theorem      161
Rook      32
Root systems      17
Sequence angle      76
Sequence degree      113
Spectral decomposition      3
Spectral moment      24 80
Spectrum      2
Spectrum Laplacian      54
Spectrum, main part      25
Spectrum, partial      95
Spectrum, Seidel      5 99
Spherical set of vectors      150
Spoke      4
Star basis      21 152
Star basis, canonical      21 192
Star basis, orthodox      193 195
Star basis, quasi-canonical      195
Star cell      151
Star cell, line      189
Star partition      21 151
Star partition, line      189
Star partition, orthodox      193 195
Star, double      212
Star, eutactic      151
Strong product      30
Subgraph, vertex-deleted      83 126
Sum of graphs      30
Switching      5
Tournament, doubly regular      131
Tournament, self-converse      130
Tree, canonical      224
Trees, co-immanantal      10
Trees, isospectral      6
Triangle, internal      50
Vector, main      97
Vertex degrees, generalized      81
Vertex ordering, admissible      195
Vertex ordering, canonical      192 196
Vertex, addition of      90
Vertex, bridging      89
Vertex, substitution, unrestricted      107
Vertices, adjacent      1
Vertices, cospectral      10 105
Vertices, cospectral pairs of      108
Vertices, similar      44
Vertices, unrestricted      10
Walk      24
Walk, closed      24
Wheel      4
Wheel, broken      64
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