Liu B., Lai H.-J. — Matrices in Combinatorics and Graph Theory (Network Theory and Applications Volume 3) :: Электронная библиотека попечительского совета мехмата МГУ

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Liu B., Lai H.-J. — Matrices in Combinatorics and Graph Theory (Network Theory and Applications Volume 3)

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Название: Matrices in Combinatorics and Graph Theory (Network Theory and Applications Volume 3)

Авторы: Liu B., Lai H.-J.

Аннотация:

The first chapter of this book provides a brief treatment of the basics of the subject. The other chapters deal with the various decompositions of non-negative matrices, Birkhoff type theorems, the study of the powers of non-negative matrices, applications of matrix methods to other combinatorial problems, and applications of combinatorial methods to matrix problems and linear algebra problems. The coverage of prerequisites has been kept to a minimum. Nevertheless, the book is basically self-contained (an Appendix provides the necessary background in linear algebra, graph theory and combinatorics). There are many exercises, all of which are accompanied by sketched solutions. Audience: The book is suitable for a graduate course as well as being an excellent reference and a valuable resource for mathematicians working in the area of combinatorial matrix theory.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Добавлена в каталог: 10.03.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(L_{t},D_{t})$ -decomposition      175
$(v,k,\lambda)$ -BIBD      169
$(v,k,\lambda)$ -SBIBD      169
$(\Gamma,b)$ -coloring      205
$r\times n$ normalized Latin rectangle      91
$\Gamma$ -colorable      205
$\Gamma$ -extendible      211
(1-3) property      227
(3-1) property      227
(m,k)-cycle      89
(r,g)-graph      5
1-Factor      219
Acyclic      234
Adjacency matrix      1
Adjacency matrix, reduced      2
Adjacent      279
Admittance matrix      3
Agree with the blocks of the matrix      261
ARC      280
Associated digraph      1
b-solution      200
Balanced incomplete block design      169
Band graph      251
BIBD      169
Bipartite decomposition      171
Bipartite digraph representation      224
Bisimplicial      246
Bloc, irreducible      143
Bloc, trivial      143
Block      168 261
Boolean matrix      101
Boolean matrix, multiplication and addition      101
Boolean rank      150
Branch      55
Canonical transformer      104
Characteristic equation      161
Characteristic polynomial      4 275
Characteristic, level      267
Characteristic, Segre      265
Characteristic, Wyre      265
Chordal      246
Chromatic number      205 280
Circular period      127
CLIQUE      280
Clique number      209 280
Cocycle space      199
Collapsible      200
Color class      204
Column sum vector      71
Combined graph      224
Compact      81
Companian matrix      161
Complement      82
Complement, fully      82
Complementary acyclic      234
Complementary term rank      235
Complementary triangular      234
Completable      250
Complete $(m_{1},m_{2},\cdot\cdot\cdot,m_{t})$       174
Complete $(m_{1},m_{2},\cdot\cdot\cdot,m_{t})$ -decomposition      174
Complete graph      280
Complete k-equipartite      86
Completion      250
Completion, nonnegative      250
Completion, positive      250
Conference graph      193
Confundable      181
Contraction      55
Convergence, index      102
Convergence, period      102
Corresponding homogenous equation      161
Cospectral graph      20
Cospectrally rooted      22
Cover      167
Cyclable      198 199
CYCLE      199 279
Cycle space      199
Cyclic vertex      55
Cyclically connected      257
Cyclically d-partite      102
Decomposable, nearly      58
Decomposable, partly      48
Decomposition, $(L_{t},D_{t})$       175
Definite Hermitian      249
Degree      279
Degree, maximum      279
Degree, minimum      279
density      57
Design, balanced incomplete block design      169
Design, symmetric balanced incomplete block design      169
Design, t-design      168
Diagonal      49
Diagonal dominant      254
Diagonal, nonzero      49
Diagonally similar      219
Difference equation      161
Digraph      280
Digraph, cyclically connected      257
Digraph, Eulerian      80
Digraph, k-cyclic      79
Digraph, minimally strong      54
Digraph, primitive      107
Digraph, square bipartite      238
Digraph, strong      281
Digraph, weakly connected      281
Digraph, weighted      217
Digraph, weighted associate      163
Directed (x,y)-walk      281
Disjoint union      280
Distinguished vertex      266
Doubly stochastic matrix      77
Doubly stochastic type      79
EDGE      279
END      279
Equation, characteristic      161
Equation, corresponding homogenous      161
Equation, difference      161
Equivalence normal form      52
Essentially different      236
Eulerian      197 204
Eulerian digraph      80
Eulerian vector      199
Even      197
Exponent, fully indecomposable      136
Exponent, Hall      142
Exponent, primitive      107
Exponent, strict fully indecomposable      137
Exponent, strict Hall      142
Exponent, weak fully indecomposable      145
Exponent, weak Hall      145
Exponent, weak primitive      145
EXTEND      250
Extremal Matrix problem      111
FISH      194
FOLLOW      251
Forbidden pair      228
Frobenius normal form      50
Frobenius Number      99
Frobenius problem      99
Fully complement      82
Fully indecomposable      49
Fully indecomposable exponent      136
Fully indecomposable exponent, strict      137
G-inverse      224
g-inverse graph      224
g-inverse graph, maximum      226
g-inverse graph, minimum      226
G-partial matrix      250
G-partial nonnegative      250
G-partial positive      250

Gauss elimination process      245
Generalized composition      22
Generalized eigenspace      266
Generalized inverse      224
Gersgorin disc      255
girth      279
Graph      279
Graph, band      251
Graph, chordal      246
Graph, combined      224
Graph, completable      250
Graph, complete      280
Graph, conference      193
Graph, connected      280
Graph, cospectral      20
Graph, directed      280
Graph, g-inverse      224
Graph, girth      279
Graph, Jordan      265
Graph, k-friendship      193
Graph, line      17
Graph, nonnegative-completable      250
Graph, perfect      181 246
Graph, perfect elimination bipartite      246
Graph, planar      280
Graph, r-regular      279
Graph, reduced      262
Graph, rooted      22
Graph, singular      266
Graph, strongly regular      190
Graph, total      17
Graph, weighted bipartite      217
Group chromatic number      206
Hadamard matrix      231
Hall exponent      142
Hall exponent, strict      142
Hall exponent, weak      145
Hall matrix      142
Handle      182
head      280
Hermitian      249
High      267
Homogenous solution      162
Imprimitive      102
Imprimitive parameters      144
Imprimitive standard form      105
In-incidence matrix      19
incidence      279
Incidence matrix      2 167
Incidence matrix, oriented      2
incident      279
Indecomposable, fully      49
Indegree      280
Independence number      181 280
Independent      277
Independent set      280
Independent vertex set      181
INDEX      266
Index of convergence      102
Index of imprimitivity      102 105
Index of maximum density      125
Induced subgraph      279
Interchange      74
Internal vertex      55 279
Invariant      75
Irreducible      48
Irreducible block      143
Join      280
Jordan Basis      266
Jordan basis, nonnegative      266
Jordan chain      266
Jordan chain, nonnegative      266
Jordan graph      265
k-colorable      204
k-critical      205
k-cyclic digraph      79
k-diameter      175
k-friendship graph      193
Kronecker product      24
kth lower multi-exponent of D      130
kth upper multi-exponent of D      130
Laplace matrix      3
Laplace matrix of a graph      3
Length      56 279
Level characteristic      267
Level diagram      266
Line      277
Line graph      17
Line rank      277
Link      279
Local switching in G with respect to $\pi$       23
Loop      279 280
M-matrix      263
Majorized by      72
Matching      167
Matrix, acyclic      234
Matrix, adjacency      1
Matrix, admittance      3
Matrix, Boolean      101
Matrix, companian      161
Matrix, complementary acyclic      234
Matrix, definite Hermitian      249
Matrix, diagonal dominant      254
Matrix, doubly stochastic      77
Matrix, essentially different      236
Matrix, Eulerian      197 204
Matrix, even      197
Matrix, fully decomposable      49
Matrix, G-partial      250
Matrix, G-partial nonnegative      250
Matrix, G-partial positive      250
Matrix, Hadamard      231
Matrix, Hall      142
Matrix, hermitian      249
Matrix, imprimitive      102
Matrix, in-incidence      19
Matrix, incidence      2 167
Matrix, irreducible      48
Matrix, Laplace      3
Matrix, M-matrix      263
Matrix, maximal      72
Matrix, nearly reducible      54
Matrix, nonnegative      275
Matrix, nonseparable      197
Matrix, out-incidence      19
Matrix, partial Hermitian      249
Matrix, partly decomposable      48
Matrix, path      177
Matrix, permutation      1
Matrix, positive      275
Matrix, primitive      102
Matrix, reducible      48
Matrix, semidefinite Hermitian      249
Matrix, separable      197
Matrix, simple      197
Matrix, spanning      197
Matrix, stochastic      77
Matrix, strict diagonal dominant      254
Matrix, strictly positive      275
Matrix, subeulerian      198
Matrix, supereulerian      198
Matrix, weakly irreducible      257
Maximal matrix      72
Maximum density      125
Maximum density, index      125
Maximum g-inverse      226
Maximum Index problem      111
Minimal cycle      252
Minimally strong digraph      54
Minimum g-inverse      226

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