{"product_id":"9783110480733","title":"Algebraic Elements of Graphs","description":"\u003cp\u003eThis 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. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cstrong\u003e\u003c\/strong\u003e \u003cp\u003e\u003cstrong\u003eContents\n\u003c\/strong\u003eAbstract Graphs\nAbstract Maps\nDuality\nOrientability\nOrientable Maps\nNonorientable Maps\nIsomorphisms of Maps\nAsymmetrization\nAsymmetrized Petal Bundles\nAsymmetrized Maps\nMaps within Symmetry\nGenus Polynomials\nCensus with Partitions\nEquations with Partitions\nUpper Maps of a Graph\nGenera of a Graph\nIsogemial Graphs\nSurface Embeddability\n\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eYanpei Liu\u003c\/strong\u003e, Beijing Jiaotong University, Beijing, China \u003c\/p\u003e Table of Content:\nPreface\nChapter 1 Abstract Graphs\n1.1 Graphs and Networks\n1.2 Surfaces\n1.3 Embeddings\n1.4 Abstract Representation\n1.5 Notes\nChapter 2 Abstract Maps\n2.1 Ground Sets\n2.2 Basic Permutations\n2.3 Conjugate Axiom\n2.4 Transitive Axiom\n2.5 Included Angles\n2.6 Notes\nChapter 3 Duality\n3.1 Dual Maps\n3.2 Deletion of an Edge\n3.3 Addition of an Edge\n3.4 Basic Transformation\n3.5 Notes\nChapter 4 Orientability\n4.1 Orientation\n4.2 Basic Equivalence\n4.3 Euler Characteristic\n4.4 Pattern Examples\n4.5 Notes\nChapter 5 Orientable Maps\n5.1 Butterflies\n5.2 Simplified Butterflies\n5.3 Reduced Rules\n5.4 Orientable Principles\n5.5 Orientable Genus\n5.6 Notes\nChapter 6 Nonorientable Maps\n6.1 Barflies\n6.2 Simplified Barflies\n6.3 Nonorientable Rules\n6.4 Nonorientable Principles\n6.5 Nonorientable Genus\n6.6 Notes\nChapter 7 Isomorphisms of Maps\n7.1 Commutativity\n7.2 Isomorphism Theorem\n7.3 Recognition\n7.4 Justification\n7.5 Pattern Examples\n7.6 Notes\nChapter 8 Asymmetrization\n8.1 Automorphisms\n8.2 Upper Bounds of Group Order\n8.3 Determination of the Group\n8.4 Rootings\n8.5 Notes\nChapter 9 Asymmetrized Petal Bundles\n9.1 Orientable Petal Bundles\n9.2 Planar Pedal Bundles\n9.3 Nonorientable Pedal Bundles\n9.4 The Number of Pedal Bundles\n9.5 Notes\nChapter 10 Asymmetrized Maps\n10.1 Orientable Equation\n10.2 Planar Rooted Maps\n10.3 Nonorientable Equation\n10.4 Gross Equation\n10.5 The Number of Rooted Maps\n10.6 Notes\nChapter 11 Maps Within Symmetry\n11.1 Symmetric Relation\n11.2 An Application\n11.3 Symmetric Principle\n11.4 General Examples\n11.5 Notes\nChapter 12 Genus Polynomials\n12.1 Associate Surfaces\n12.2 Layer Division of a Surface\n12.3 Handle Polynomials\n12.4 Crosscap Polynomials\n12.5 Notes\nChapter 13 Census with Partitions\n13.1 Planted Trees\n13.2 Hamiltonian Cubic Maps\n13.3 Halin Maps\n13.4 Biboundary Inner Rooted Maps\n13.5 General Maps\n13.6 Pan-Flowers\n13.7 Notes\nChapter 14 Equations with Partitions\n14.1 The Meson Functional\n14.2 General Maps on the Sphere\n14.3 Nonseparable Maps on the Sphere\n14.4 Maps Without Cut-Edge on Surfaces\n14.5 Eulerian Maps on the Sphere\n14.6 Eulerian Maps on Surfaces\n14.7 Notes\nChapter 15 Upper Maps of a Graph\n15.1 Semi-Automorphisms on a Graph\n15.2 Automorphisms on a Graph\n15.3 Relationships\n15.4 Upper Maps with Symmetry\n15.5 Via Asymmetrized Upper Maps\n15.6 Notes\nChapter 16 Genera of Graphs\n16.1 A Recursion Theorem\n16.2 Maximum Genus\n16.3 Minimum Genus\n16.4 Average Genus\n16.5 Thickness\n16.6 Interlacedness\n16.7 Notes\nChapter 17 Isogemial Graphs\n17.1 Basic Concepts\n17.2 Two Operations\n17.3 Isogemial Theorem\n17.4 Nonisomorphic Isogemial Graphs\n17.5 Notes\nChapter 18 Surface Embeddability\n18.1 Via Tree-Travels\n18.2 Via Homology\n18.3 Via Joint Trees\n18.4 Via Configurations\n18.5 Notes\nAppendix 1 Concepts of Polyhedra, Surfaces, Embeddings and Maps\nAppendix 2 Table of Genus Polynomials for Embeddings and Maps of Small Size\nAppendix 3 Atlas of Rooted and Unrooted Maps for Small Graphs\nBibliography","brand":"De Gruyter","offers":[{"title":"Default Title","offer_id":42600288616523,"sku":"00000_00000_00000_00000","price":6952.04,"currency_code":"THB","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0641\/0023\/7387\/files\/9783110480733-1.jpg?v=1783500933","url":"https:\/\/kinokuniya.co.th\/ja\/products\/9783110480733","provider":"Books Kinokuniya Thailand","version":"1.0","type":"link"}