Record:   Prev Next
作者 Liu, Yanpei
書名 Topological Theory of Graphs
出版項 Berlin/Boston : De Gruyter, Inc., 2017
©2017
國際標準書號 9783110479492 (electronic bk.)
9783110476699
book jacket
說明 1 online resource (370 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Intro -- Preface to DG Edition -- Preface to USTC Edition -- Contents -- 1 Preliminaries -- 1.1 Sets and relations -- 1.2 Partitions and permutations -- 1.3 Graphs and networks -- 1.4 Groups and spaces -- 1.5 Notes -- 2 Polyhedra -- 2.1 Polygon double covers -- 2.2 Supports and skeletons -- 2.3 Orientable polyhedra -- 2.4 Non-orientable polyhedra -- 2.5 Classic polyhedra -- 2.6 Notes -- 3 Surfaces -- 3.1 Polyhegons -- 3.2 Surface closed curve axiom -- 3.3 Topological transformations -- 3.4 Complete invariants -- 3.5 Graphs on surfaces -- 3.6 Up-embeddability -- 3.7 Notes -- 4 Homology on Polyhedra -- 4.1 Double cover by travels -- 4.2 Homology -- 4.3 Cohomology -- 4.4 Bicycles -- 4.5 Notes -- 5 Polyhedra on the Sphere -- 5.1 Planar polyhedra -- 5.2 Jordan closed-curve axiom -- 5.3 Uniqueness -- 5.4 Straight-line representations -- 5.5 Convex representation -- 5.6 Notes -- 6 Automorphisms of a Polyhedron -- 6.1 Automorphisms of polyhedra -- 6.2 Eulerian and non-Eulerian codes -- 6.3 Determination of automorphisms -- 6.4 Asymmetrization -- 6.5 Notes -- 7 Gauss Crossing Sequences -- 7.1 Crossing polyhegons -- 7.2 Dehn's transformation -- 7.3 Algebraic principles -- 7.4 Gauss crossing problem -- 7.5 Notes -- 8 Cohomology on Graphs -- 8.1 Immersions -- 8.2 Realization of planarity -- 8.3 Reductions -- 8.4 Planarity auxiliary graphs -- 8.5 Basic conclusions -- 8.6 Notes -- 9 Embeddability on Surfaces -- 9.1 Joint tree model -- 9.2 Associate polyhegons -- 9.3 A transformation -- 9.4 Criteria of embeddability -- 9.5 Notes -- 10 Embeddings on Sphere -- 10.1 Left and right determinations -- 10.2 Forbidden configurations -- 10.3 Basic order characterization -- 10.4 Number of planar embeddings -- 10.5 Notes -- 11 Orthogonality on Surfaces -- 11.1 Definitions -- 11.2 On surfaces of genus zero -- 11.3 Surface models -- 11.4 On surfaces of genus not zero
11.5 Notes -- 12 Net Embeddings -- 12.1 Definitions -- 12.2 Face admissibility -- 12.3 General criterion -- 12.4 Special criteria -- 12.5 Notes -- 13 Extremality on Surfaces -- 13.1 Maximal genus -- 13.2 Minimal genus -- 13.3 Shortest embedding -- 13.4 Thickness -- 13.5 Crossing number -- 13.6 Minimal bend -- 13.7 Minimal area -- 13.8 Notes -- 14 Matroidal Graphicness -- 14.1 Definitions -- 14.2 Binary matroids -- 14.3 Regularity -- 14.4 Graphicness -- 14.5 Cographicness -- 14.6 Notes -- 15 Knot Polynomials -- 15.1 Definitions -- 15.2 Knot diagram -- 15.3 Tutte polynomial -- 15.4 Pan-polynomial -- 15.5 Jones Polynomial -- 15.6 Notes -- Bibliography -- Subject Index -- Author Index
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Liu, Yanpei Topological Theory of Graphs Berlin/Boston : De Gruyter, Inc.,c2017 9783110476699
主題 Graphic methods
Electronic books
Alt Author University of Science & Technology, University of Science &
Record:   Prev Next