Matrices in combinatorics and graph theory:
"The first chapter of the book provides a brief treatment of the basics. The other chapters deal with the various decompositions of nonnegative matrices, Birkhoff type theorems, the study of the powers of nonnegative matrices, applications of matrix methods to other combinatorial problems, and...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2000
|
| Schriftenreihe: | Network theory and applications
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "The first chapter of the book provides a brief treatment of the basics. The other chapters deal with the various decompositions of nonnegative matrices, Birkhoff type theorems, the study of the powers of nonnegative 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." "The book is suitable for a graduate course as well as being a reference and a resource for mathematicians working in the area of combinatorial matrix theory."--BOOK JACKET. |
| Beschreibung: | XI, 310 S. graph. Darst. |
| ISBN: | 0792364694 |
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Datensatz im Suchindex
| _version_ | 1804128740057284608 |
|---|---|
| adam_text | MATRICES IN COMBINATORICS AND GRAPH THEORY BY BOLIAN LIU DEPARTMENT OF
MATHEMATICS, SOUTH CHINA NORMAL UNIVERSITY, GUANGZHOU, P. R. CHINA AND
HONG-JIAN LAI DEPARTMENT OF MATHEMATICS, WEST VIRGINIA UNIVERSITY,
MORGANTOWN, WEST VIRGINIA, U.S.A. KLUWER ACADEMIC PUBLISHERS DORDRECHT /
BOSTON / LONDON CONTENTS FOREWORD IX PREFACE XI 1 MATRICES AND GRAPHS 1
1.1 THE BASICS 1 1.2 THE SPECTRUM OF A GRAPH 5 1.3 ESTIMATING THE
EIGENVALUES OF A GRAPH 12 1.4 LINE GRAPHS AND TOTAL GRAPHS 17 1.5
COSPECTRAL GRAPHS 20 1.6 SPECTRAL RADIUS 24 1.7 EXERCISES 38 1.8 HINTS
FOR EXERCISES 41 2 COMBINATORIAL PROPERTIES OF MATRICES 47 2.1
IRREDUCIBLE AND FULLY INDECOMPOSABLE MATRICES 48 2.2 STANDARD FORMS 50
2.3 NEARLY REDUCIBLE MATRICES 54 2.4 NEARLY DECOMPOSABLE MATRICES , 58
2.5 PERMANENT 61 2.6 THE CLASS W(R, S) 71 2.7 STOCHASTIC MATRICES AND
DOUBLY STOCHASTIC MATRICES 77 2.8 BIRKHOFF TYPE THEOREMS 81 2.9 EXERCISE
90 2.10 HINTS FOR EXERCISES 92 3 POWERS OF NONNEGATIVE MATRICES 97 3.1
THE FROBENIUS DIOPHANTINE PROBLEM 97 3.2 THE PERIOD AND THE INDEX OF A
BOOLEAN MATRIX 101 VI CONTENTS 3.3 THE PRIMITIVE EXPONENT 107 3.4 THE
INDEX OF CONVERGENCE OF IRREDUCIBLE NONPRIMITIVE MATRICES 114 3.5 THE
INDEX OF CONVERGENCE OF REDUCIBLE NONPRIMITIVE MATRICES 120 3.6 INDEX OF
DENSITY * 125 3.7 GENERALIZED EXPONENTS OF PRIMITIVE MATRICES 129 3.8
FULLY INDECOMPOSABLE EXPONENTS AND HALL EXPONENTS 136 3.9 PRIMITIVE
EXPONENT AND OTHER PARAMETERS 146 3.10 EXERCISES 150 3.11 HINT FOR
EXERCISES 153 4 MATRICES IN COMBINATORIAL PROBLEMS 161 4.1 MATRIX
SOLUTIONS FOR DIFFERENCE EQUATIONS 161 4.2 MATRICES IN SOME
COMBINATORIAL CONFIGURATIONS 166 4.3 DECOMPOSITION OF GRAPHS 171 4.4
MATRIX-TREE THEOREMS 176 4.5 SHANNON CAPACITY 180 4.6 STRONGLY REGULAR
GRAPHS 190 4.7 EULERIAN PROBLEMS 196 4.8 THE CHROMATIC NUMBER 204 4.9
EXERCISES 210 4.10 HINTS FOR EXERCISES 212 5 COMBINATORIAL ANALYSIS IN
MATRICES 217 5.1 COMBINATORIAL REPRESENTATION OF MATRICES AND
DETERMINANTS 217 5.2 COMBINATORIAL PROOFS IN LINEAR ALGEBRA 221 5.3
GENERALIZED INVERSE OF A BOOLEAN MATRIX 224 5.4 MAXIMUM DETERMINANT OF A
(0,1) MATRIX 230 5.5 REARRANGEMENT OF (0,1) MATRICES 236 5.6 PERFECT
ELIMINATION SCHEME 245 5.7 COMPLETIONS OF PARTIAL HERMITIAN MATRICES 249
5.8 ESTIMATION OF THE EIGENVALUES OF A MATRIX 253 5.9 M-MATRICES 261
5.10 EXERCISES 271 5.11 HINTS FOR EXERCISES 272 6 APPENDIX 275 6.1
LINEAR ALGEBRA AND MATRICES 275 6.2 THE TERM RANK AND THE LINE RANK OF A
MATRIX 277 6.3 GRAPH THEORY 279 CONTENTS VII INDEX 283 BIBLIOGRAPHY 291
|
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| id | DE-604.BV013896927 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:02Z |
| institution | BVB |
| isbn | 0792364694 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009509631 |
| oclc_num | 44173053 |
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| physical | XI, 310 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | Kluwer Acad. Publ. |
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| series | Network theory and applications |
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| spelling | Liu, Bolian Verfasser aut Matrices in combinatorics and graph theory by Bolian Liu and Hong-Jian Lai Dordrecht [u.a.] Kluwer Acad. Publ. 2000 XI, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Network theory and applications 3 "The first chapter of the book provides a brief treatment of the basics. The other chapters deal with the various decompositions of nonnegative matrices, Birkhoff type theorems, the study of the powers of nonnegative 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." "The book is suitable for a graduate course as well as being a reference and a resource for mathematicians working in the area of combinatorial matrix theory."--BOOK JACKET. Combinatieleer gtt Grafentheorie gtt Combinatorial analysis Graph theory Matrices Kombinatorische Graphentheorie (DE-588)4164748-8 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 s Kombinatorische Graphentheorie (DE-588)4164748-8 s DE-604 Lai, Hong-Jian Verfasser aut Network theory and applications 3 (DE-604)BV014100569 3 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009509631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Bolian Lai, Hong-Jian Matrices in combinatorics and graph theory Network theory and applications Combinatieleer gtt Grafentheorie gtt Combinatorial analysis Graph theory Matrices Kombinatorische Graphentheorie (DE-588)4164748-8 gnd Matrizentheorie (DE-588)4128970-5 gnd |
| subject_GND | (DE-588)4164748-8 (DE-588)4128970-5 |
| title | Matrices in combinatorics and graph theory |
| title_auth | Matrices in combinatorics and graph theory |
| title_exact_search | Matrices in combinatorics and graph theory |
| title_full | Matrices in combinatorics and graph theory by Bolian Liu and Hong-Jian Lai |
| title_fullStr | Matrices in combinatorics and graph theory by Bolian Liu and Hong-Jian Lai |
| title_full_unstemmed | Matrices in combinatorics and graph theory by Bolian Liu and Hong-Jian Lai |
| title_short | Matrices in combinatorics and graph theory |
| title_sort | matrices in combinatorics and graph theory |
| topic | Combinatieleer gtt Grafentheorie gtt Combinatorial analysis Graph theory Matrices Kombinatorische Graphentheorie (DE-588)4164748-8 gnd Matrizentheorie (DE-588)4128970-5 gnd |
| topic_facet | Combinatieleer Grafentheorie Combinatorial analysis Graph theory Matrices Kombinatorische Graphentheorie Matrizentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009509631&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014100569 |
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