LEADER 03336nam 2200577 450 001 9910795044803321 005 20230809234344.0 010 $a3-11-048075-1 010 $a3-11-048184-7 024 7 $a10.1515/9783110481846 035 $a(CKB)4340000000203637 035 $a(MiAaPQ)EBC5049532 035 $a(DE-B1597)466991 035 $a(OCoLC)1004878499 035 $a(DE-B1597)9783110481846 035 $a(Au-PeEL)EBL5049532 035 $a(CaPaEBR)ebr11443177 035 $a(CaONFJC)MIL1036857 035 $a(OCoLC)1004555581 035 $a(EXLCZ)994340000000203637 100 $a20171016h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aAlgebraic elements of graphs /$fYanpei Liu 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (410 pages) $cillustrations 311 $a3-11-048073-5 320 $aIncludes bibliographical references and indexes. 327 $tFrontmatter --$tPreface (DG Edition) --$tPreface (USTC Edition) --$tContents --$t1. Abstract Graphs --$t2. Abstract Maps --$t3. Duality --$t4. Orientability --$t5. Orientable Maps --$t6. Nonorientable Maps --$t7. Isomorphisms of Maps --$t8. Asymmetrization --$t9. Asymmetrized Petal Bundles --$t10. Asymmetrized Maps --$t11. Maps within Symmetry --$t12. Genus Polynomials --$t13. Census with Partitions --$t14. Equations with Partitions --$t15. Upper Maps of a Graph --$t16. Genera of a Graph --$t17. Isogemial Graphs --$t18. Surface Embeddability --$tAppendix 1: Concepts of Polyhedra, Surfaces, Embeddings and Maps --$tAppendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size --$tAppendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs --$tBibliography --$tAuthor Index --$tSubject Index 330 $aThis 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 Embeddability 606 $aRepresentations of graphs 606 $aRepresentations of algebras 606 $aAssociative algebras 615 0$aRepresentations of graphs. 615 0$aRepresentations of algebras. 615 0$aAssociative algebras. 676 $a511.5 700 $aLiu$b Yanpei$01134336 701 $aUniversity of Science and Technology China Press$01495625 712 02$aUniversity of Science and Technology China Press. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910795044803321 996 $aAlgebraic elements of graphs$93719763 997 $aUNINA