03336nam 2200577 450 991079504480332120230809234344.03-11-048075-13-11-048184-710.1515/9783110481846(CKB)4340000000203637(MiAaPQ)EBC5049532(DE-B1597)466991(OCoLC)1004878499(DE-B1597)9783110481846(Au-PeEL)EBL5049532(CaPaEBR)ebr11443177(CaONFJC)MIL1036857(OCoLC)1004555581(EXLCZ)99434000000020363720171016h20172017 uy 0engurcnu||||||||rdacontentrdamediardacarrierAlgebraic elements of graphs /Yanpei LiuBerlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2017.©20171 online resource (410 pages) illustrations3-11-048073-5 Includes bibliographical references and indexes.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 IndexThis 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. ContentsAbstract GraphsAbstract MapsDualityOrientabilityOrientable MapsNonorientable MapsIsomorphisms of MapsAsymmetrizationAsymmetrized Petal BundlesAsymmetrized MapsMaps within SymmetryGenus PolynomialsCensus with PartitionsEquations with PartitionsUpper Maps of a GraphGenera of a GraphIsogemial GraphsSurface EmbeddabilityRepresentations of graphsRepresentations of algebrasAssociative algebrasRepresentations of graphs.Representations of algebras.Associative algebras.511.5Liu Yanpei1134336University of Science and Technology China Press1495625University of Science and Technology China Press.MiAaPQMiAaPQMiAaPQBOOK9910795044803321Algebraic elements of graphs3719763UNINA