Algebraic Elements of Graphs /:
This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications w...
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| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston :
De Gruyter,
[2017]
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author's original work on graph embeddings, this book is an essential reference for researchers in graph theory. |
| Physical Description: | 1 online resource (xiv, 409 pages) : illustrations |
| Bibliography: | Includes bibliographical references and indexes. |
| ISBN: | 9783110480757 3110480751 3110481847 9783110481846 |
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MARC
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| 245 | 1 | 0 | |a Algebraic Elements of Graphs / |c Yanpei Liu. |
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| 505 | 0 | 0 | |t Frontmatter -- |t Preface (DG Edition) -- |t Preface (USTC Edition) -- |t Contents -- |t 1. Abstract Graphs -- |t 2. Abstract Maps -- |t 3. Duality -- |t 4. Orientability -- |t 5. Orientable Maps -- |t 6. Nonorientable Maps -- |t 7. Isomorphisms of Maps -- |t 8. Asymmetrization -- |t 9. Asymmetrized Petal Bundles -- |t 10. Asymmetrized Maps -- |t 11. Maps within Symmetry -- |t 12. Genus Polynomials -- |t 13. Census with Partitions -- |t 14. Equations with Partitions -- |t 15. Upper Maps of a Graph -- |t 16. Genera of a Graph -- |t 17. Isogemial Graphs -- |t 18. Surface Embeddability -- |t Appendix 1: Concepts of Polyhedra, Surfaces, Embeddings and Maps -- |t Appendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size -- |t Appendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs -- |t Bibliography -- |t Author Index -- |t Subject Index. |
| 546 | |a In English. | ||
| 588 | 0 | |a Online resource; title from PDF title page (publisher's Web site, viewed 13. Sep 2017). | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 520 | |a This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author's original work on graph embeddings, this book is an essential reference for researchers in graph theory. | ||
| 650 | 0 | |a Representations of graphs. |0 http://id.loc.gov/authorities/subjects/sh85112943 | |
| 650 | 0 | |a Representations of algebras. |0 http://id.loc.gov/authorities/subjects/sh85112938 | |
| 650 | 0 | |a Associative algebras. |0 http://id.loc.gov/authorities/subjects/sh85008821 | |
| 650 | 6 | |a Représentations de graphes. | |
| 650 | 6 | |a Représentations des algèbres. | |
| 650 | 6 | |a Algèbres associatives. | |
| 650 | 7 | |a MATHEMATICS |x Essays. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Pre-Calculus. |2 bisacsh | |
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| 650 | 7 | |a Associative algebras |2 fast | |
| 650 | 7 | |a Representations of algebras |2 fast | |
| 650 | 7 | |a Representations of graphs |2 fast | |
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| 653 | |a (BISAC Subject Heading)MAT002000: MAT002000 MATHEMATICS / Algebra / General | ||
| 653 | |a (BISAC Subject Heading)MAT012000: MAT012000 MATHEMATICS / Geometry / General | ||
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| author | Liu, Yanpei |
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| contents | Frontmatter -- Preface (DG Edition) -- Preface (USTC Edition) -- Contents -- 1. Abstract Graphs -- 2. Abstract Maps -- 3. Duality -- 4. Orientability -- 5. Orientable Maps -- 6. Nonorientable Maps -- 7. Isomorphisms of Maps -- 8. Asymmetrization -- 9. Asymmetrized Petal Bundles -- 10. Asymmetrized Maps -- 11. Maps within Symmetry -- 12. Genus Polynomials -- 13. Census with Partitions -- 14. Equations with Partitions -- 15. Upper Maps of a Graph -- 16. Genera of a Graph -- 17. Isogemial Graphs -- 18. Surface Embeddability -- Appendix 1: Concepts of Polyhedra, Surfaces, Embeddings and Maps -- Appendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size -- Appendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs -- Bibliography -- Author Index -- Subject Index. |
| ctrlnum | (OCoLC)1004878499 |
| dewey-full | 510 |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
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| discipline | Mathematik |
| format | Electronic eBook |
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Abstract Graphs --</subfield><subfield code="t">2. Abstract Maps --</subfield><subfield code="t">3. Duality --</subfield><subfield code="t">4. Orientability --</subfield><subfield code="t">5. Orientable Maps --</subfield><subfield code="t">6. Nonorientable Maps --</subfield><subfield code="t">7. Isomorphisms of Maps --</subfield><subfield code="t">8. Asymmetrization --</subfield><subfield code="t">9. Asymmetrized Petal Bundles --</subfield><subfield code="t">10. Asymmetrized Maps --</subfield><subfield code="t">11. Maps within Symmetry --</subfield><subfield code="t">12. Genus Polynomials --</subfield><subfield code="t">13. Census with Partitions --</subfield><subfield code="t">14. Equations with Partitions --</subfield><subfield code="t">15. Upper Maps of a Graph --</subfield><subfield code="t">16. Genera of a Graph --</subfield><subfield code="t">17. Isogemial Graphs --</subfield><subfield code="t">18. 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| id | ZDB-4-EBA-on1004878499 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:43:57Z |
| institution | BVB |
| isbn | 9783110480757 3110480751 3110481847 9783110481846 |
| language | English |
| oclc_num | 1004878499 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 409 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | De Gruyter, |
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| spelling | Liu, Yanpei, author. https://id.oclc.org/worldcat/entity/E39PCjr6YQdywGXC6mFbFb8BKb http://id.loc.gov/authorities/names/n87935364 Algebraic Elements of Graphs / Yanpei Liu. Berlin ; Boston : De Gruyter, [2017] ©2017 1 online resource (xiv, 409 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier text file Frontmatter -- Preface (DG Edition) -- Preface (USTC Edition) -- Contents -- 1. Abstract Graphs -- 2. Abstract Maps -- 3. Duality -- 4. Orientability -- 5. Orientable Maps -- 6. Nonorientable Maps -- 7. Isomorphisms of Maps -- 8. Asymmetrization -- 9. Asymmetrized Petal Bundles -- 10. Asymmetrized Maps -- 11. Maps within Symmetry -- 12. Genus Polynomials -- 13. Census with Partitions -- 14. Equations with Partitions -- 15. Upper Maps of a Graph -- 16. Genera of a Graph -- 17. Isogemial Graphs -- 18. Surface Embeddability -- Appendix 1: Concepts of Polyhedra, Surfaces, Embeddings and Maps -- Appendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size -- Appendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs -- Bibliography -- Author Index -- Subject Index. In English. Online resource; title from PDF title page (publisher's Web site, viewed 13. Sep 2017). Includes bibliographical references and indexes. This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author's original work on graph embeddings, this book is an essential reference for researchers in graph theory. Representations of graphs. http://id.loc.gov/authorities/subjects/sh85112943 Representations of algebras. http://id.loc.gov/authorities/subjects/sh85112938 Associative algebras. http://id.loc.gov/authorities/subjects/sh85008821 Représentations de graphes. Représentations des algèbres. Algèbres associatives. MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Associative algebras fast Representations of algebras fast Representations of graphs fast (Produktform)Electronic book text (Zielgruppe)Fachpublikum/ Wissenschaft (BISAC Subject Heading)MAT036000 (BISAC Subject Heading)MAT038000: MAT038000 MATHEMATICS / Topology (BISAC Subject Heading)MAT002000: MAT002000 MATHEMATICS / Algebra / General (BISAC Subject Heading)MAT012000: MAT012000 MATHEMATICS / Geometry / General (VLB-WN)9620 (Produktrabattgruppe)PR: rabattbeschränkt/Bibliothekswerke University of Science and Technology China Press. Print version: 9783110481853 Print version: 9783110480757 Print version: 9783110480733 Print version: Liu, Yanpei, 1939- Algebraic elements of graphs. Berlin ; Boston : Walter de Gruyter GmbH, [2017] 9783110480733 (DLC) 2017042339 (OCoLC)985076036 |
| spellingShingle | Liu, Yanpei Algebraic Elements of Graphs / Frontmatter -- Preface (DG Edition) -- Preface (USTC Edition) -- Contents -- 1. Abstract Graphs -- 2. Abstract Maps -- 3. Duality -- 4. Orientability -- 5. Orientable Maps -- 6. Nonorientable Maps -- 7. Isomorphisms of Maps -- 8. Asymmetrization -- 9. Asymmetrized Petal Bundles -- 10. Asymmetrized Maps -- 11. Maps within Symmetry -- 12. Genus Polynomials -- 13. Census with Partitions -- 14. Equations with Partitions -- 15. Upper Maps of a Graph -- 16. Genera of a Graph -- 17. Isogemial Graphs -- 18. Surface Embeddability -- Appendix 1: Concepts of Polyhedra, Surfaces, Embeddings and Maps -- Appendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size -- Appendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs -- Bibliography -- Author Index -- Subject Index. Representations of graphs. http://id.loc.gov/authorities/subjects/sh85112943 Representations of algebras. http://id.loc.gov/authorities/subjects/sh85112938 Associative algebras. http://id.loc.gov/authorities/subjects/sh85008821 Représentations de graphes. Représentations des algèbres. Algèbres associatives. MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Associative algebras fast Representations of algebras fast Representations of graphs fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85112943 http://id.loc.gov/authorities/subjects/sh85112938 http://id.loc.gov/authorities/subjects/sh85008821 |
| title | Algebraic Elements of Graphs / |
| title_alt | Frontmatter -- Preface (DG Edition) -- Preface (USTC Edition) -- Contents -- 1. Abstract Graphs -- 2. Abstract Maps -- 3. Duality -- 4. Orientability -- 5. Orientable Maps -- 6. Nonorientable Maps -- 7. Isomorphisms of Maps -- 8. Asymmetrization -- 9. Asymmetrized Petal Bundles -- 10. Asymmetrized Maps -- 11. Maps within Symmetry -- 12. Genus Polynomials -- 13. Census with Partitions -- 14. Equations with Partitions -- 15. Upper Maps of a Graph -- 16. Genera of a Graph -- 17. Isogemial Graphs -- 18. Surface Embeddability -- Appendix 1: Concepts of Polyhedra, Surfaces, Embeddings and Maps -- Appendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size -- Appendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs -- Bibliography -- Author Index -- Subject Index. |
| title_auth | Algebraic Elements of Graphs / |
| title_exact_search | Algebraic Elements of Graphs / |
| title_full | Algebraic Elements of Graphs / Yanpei Liu. |
| title_fullStr | Algebraic Elements of Graphs / Yanpei Liu. |
| title_full_unstemmed | Algebraic Elements of Graphs / Yanpei Liu. |
| title_short | Algebraic Elements of Graphs / |
| title_sort | algebraic elements of graphs |
| topic | Representations of graphs. http://id.loc.gov/authorities/subjects/sh85112943 Representations of algebras. http://id.loc.gov/authorities/subjects/sh85112938 Associative algebras. http://id.loc.gov/authorities/subjects/sh85008821 Représentations de graphes. Représentations des algèbres. Algèbres associatives. MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Associative algebras fast Representations of algebras fast Representations of graphs fast |
| topic_facet | Representations of graphs. Representations of algebras. Associative algebras. Représentations de graphes. Représentations des algèbres. Algèbres associatives. MATHEMATICS Essays. MATHEMATICS Pre-Calculus. MATHEMATICS Reference. Associative algebras Representations of algebras Representations of graphs |
| work_keys_str_mv | AT liuyanpei algebraicelementsofgraphs AT universityofscienceandtechnologychinapress algebraicelementsofgraphs |