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Algebraic Elements of Graphs / Yanpei Liu.

By: Contributor(s): Material type: TextTextPublisher: Berlin ; Boston : De Gruyter, [2017]Copyright date: ©2017Description: 1 online resource (xiv, 409 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110480757
  • 3110480751
  • 3110481847
  • 9783110481846
Subject(s): Genre/Form: Additional physical formats: Print version:: No title; Print version:: No title; Print version:: No title; Print version:: Algebraic elements of graphs.DDC classification:
  • 510
LOC classification:
  • QA219
Other classification:
  • 510
Online resources:
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.
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.
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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.

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