Download or read book Graphs and Polyhedra written by A. M. H. Gerards and published by . This book was released on 1990 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
Download or read book Topological Theory of Graphs written by Yanpei Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces polyhedra as a tool for graph theory and discusses their properties and applications in solving the Gauss crossing problem. The discussion is extended to embeddings on manifolds, particularly to surfaces of genus zero and non-zero via the joint tree model, along with solution algorithms. Given its rigorous approach, this book would be of interest to researchers in graph theory and discrete mathematics.
Download or read book Convex Polyhedra written by A.D. Alexandrov and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.
Download or read book Compositions of Graphs and Polyhedra written by F. Barahona and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Euler s Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Download or read book Polyhedra written by Peter R. Cromwell and published by Cambridge University Press. This book was released on 1997 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.
Download or read book Compositions of Graphs and Polyhedra written by Francisco Barahona and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graphs on Surfaces written by Bojan Mohar and published by Johns Hopkins University Press. This book was released on 2001-08-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph theory is an area of its own with many deep results and beautiful open problems. Graph theory has numerous applications in almost every field of science and has attracted new interest because of its relevance to such technological problems as computer and telephone networking and, of course, the internet. In this new book in the Johns Hopkins Studies in the Mathematical Science series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces. Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. Among the basic results discussed are Kuratowski's theorem and other planarity criteria, the Jordan Curve Theorem and some of its extensions, the classification of surfaces, and the Heffter-Edmonds-Ringel rotation principle, which makes it possible to treat graphs on surfaces in a purely combinatorial way. The genus of a graph, contractability of cycles, edge-width, and face-width are treated purely combinatorially, and several results related to these concepts are included. The extension by Robertson and Seymour of Kuratowski's theorem to higher surfaces is discussed in detail, and a shorter proof is presented. The book concludes with a survey of recent developments on coloring graphs on surfaces.
Download or read book The Representation of Planar Graphs by Convex Polyhedra written by Thomas Andrew Brown and published by . This book was released on 1960 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Shaping Space written by Marjorie Senechal and published by Springer Science & Business Media. This book was released on 2013-03-22 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is based off of the very popular Shaping Space: A Polyhedral Approach, first published twenty years ago. The book is expanded and updated to include new developments, including the revolutions in visualization and model-making that the computer has wrought. Shaping Space is an exuberant, richly-illustrated, interdisciplinary guide to three-dimensional forms, focusing on the suprisingly diverse world of polyhedra. Geometry comes alive in Shaping Space, as a remarkable range of geometric ideas is explored and its centrality in our cultre is persuasively demonstrated. The book is addressed to designers, artists, architects, engineers, chemists, computer scientists, mathematicians, bioscientists, crystallographers, earth scientists, and teachers at all levels—in short, to all scholars and educators interested in, and working with, two- and three-dimensinal structures and patterns.
Download or read book Compositions of graphs and polyhedra written by Francisco Barahona and published by . This book was released on 1987 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Chemical Graphs written by Michel Deza and published by . This book was released on 2014-05-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical tools for the study of generalisations of graphs appearing in the modelling of molecular structures.
Download or read book Graphs rings and polyhedra written by Isidoro Gitler and published by . This book was released on 2011 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scale isometric Polytopal Graphs in Hypercubes and Cubic Lattices written by M. Deza and published by World Scientific. This book was released on 2004 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph identifies polytopes that are ?combinatorially ?1-embeddable?, within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to ??2-prominent? affine polytopal objects.The lists of polytopal graphs in the book come from broad areas of geometry, crystallography and graph theory. The book concentrates on such concise and, as much as possible, independent definitions. The scale-isometric embeddability ? the main unifying question, to which those lists are subjected ? is presented with the minimum of technicalities.
Download or read book Submodular Functions Graphs and Integer Polyhedra written by Giles, Frederick Richard and published by 1975.. This book was released on 1975 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is a study of the faces of certain combinatorially defined polyhedra. In particular, we examine the vertices and facets of these polyhedra. Chapter 2 contains the essential mathematical background in polyhedral theory, linear programming and graph theory. We also discuss the existence of an integer-valued optimum solution to a linear program. This is essential for determining that the vertices of certain polyhedra are integer-valued, and for establishing related combinatorial min-max relations. Chapter 3 is the a application of the results of Chapter 4 to the polymatroid aspects of matroid theory. We characterize the vertices and the facets of the intersection of two matroid polyhedra. We use the characterization of the facets of this intersection to derive a graph theoretic description of the facets of the polyhedron associated with branchings in a graph. In Chapter 5 we discuss certain polyhedra which can be associated with strong k-covers and strong k-matchings of an acyclic graph. By proving the existence of integer¥valued optimum solutions to particular primal-dual pairs of linear programs we are able to demonstrate certain combinatorial min-max relations. Chapter 6 is a unification of the polyhedra described in Chapters 4 and 5, We give a combinatorial definition of a class of polyhedra which includes polymatroid intersection and the polyhedra associated with strong k-covers and strong k-matchings of an acyclic graph. We establish the existence of integer-valued optimum solutions to certain dual linear programs and thereby draw conclusions concerning the integrality of the vertices of particular polyhedra within this class. The applications include establishing the integrality of the vertices of the intersection of two integral polymatroids and the integrality of the vertices of strong k-cover and strong k-matching polyhedra. Chapter 7 is a discussion of the facets of polyhedra defined in Chapter 6 and we obtain a description of the facets of a subclass of these polyhedra which includes a description of the facets of the intersection of two polymatroids and the facets of strong k-cover and strong k-matching polyhedra.
Download or read book Graphical Enumeration written by Frank Harary and published by Elsevier. This book was released on 2014-05-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical Enumeration deals with the enumeration of various kinds of graphs. Topics covered range from labeled enumeration and George Pólya's theorem to rooted and unrooted trees, graphs and digraphs, and power group enumeration. Superposition, blocks, and asymptotics are also discussed. A number of unsolved enumeration problems are presented. Comprised of 10 chapters, this book begins with an overview of labeled graphs, followed by a description of the basic enumeration theorem of Pólya. The next three chapters count an enormous variety of trees, graphs, and digraphs. The Power Group Enumeration Theorem is then described together with some of its applications, including the enumeration of self-complementary graphs and digraphs and finite automata. Two other chapters focus on the counting of superposition and blocks, while another chapter is devoted to asymptotic numbers that are developed for several different graphical structures. The book concludes with a comprehensive definitive list of unsolved graphical enumeration problems. This monograph will be of interest to both students and practitioners of mathematics.
