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  • 1
    Online Resource
    Online Resource
    Magic Graphs (2001)
    Boston, MA :Birkhäuser Boston :
    Details
    UID:
    almahu_9947362876002882
    Format: XIV, 146 p. , online resource.
    ISBN: 9781461201236
    Content: Magic labelings Magic squares are among the more popular mathematical recreations. Their origins are lost in antiquity; over the years, a number of generalizations have been proposed. In the early 1960s, Sedlacek asked whether "magic" ideas could be applied to graphs. Shortly afterward, Kotzig and Rosa formulated the study of graph label­ ings, or valuations as they were first called. A labeling is a mapping whose domain is some set of graph elements - the set of vertices, for example, or the set of all vertices and edges - whose range was a set of positive integers. Various restrictions can be placed on the mapping. The case that we shall find most interesting is where the domain is the set of all vertices and edges of the graph, and the range consists of positive integers from 1 up to the number of vertices and edges. No repetitions are allowed. In particular, one can ask whether the set of labels associated with any edge - the label on the edge itself, and those on its endpoints - always add up to the same sum. Kotzig and Rosa called such a labeling, and the graph possessing it, magic. To avoid confusion with the ideas of Sedlacek and the many possible variations, we would call it an edge-magic total labeling.
    Note: 1 Preliminaries -- 1.1 Magic -- 1.2 Graphs -- 1.3 Labelings -- 1.4 Magic labeling -- 1.5 Some applications of magic labelings -- 2 Edge-Magic Total Labelings -- 2.1 Basic ideas -- 2.2 Graphs with no edge-magic total labeling -- 2.3 Cliques and complete graphs -- 2.4 Cycles -- 2.5 Complete bipartite graphs -- 2.6 Wheels -- 2.7 Trees -- 2.8 Disconnected graphs -- 2.9 Strong edge-magic total labelings -- 2.10 Edge-magic injections -- 3 Vertex-Magic Total Labelings -- 3.1 Basic ideas -- 3.2 Regular graphs -- 3.3 Cycles and paths -- 3.4 Vertex-magic total labelings of wheels -- 3.5 Vertex-magic total labelings of complete bipartite graphs -- 3.6 Graphs with vertices of degree one -- 3.7 The complete graphs -- 3.8 Disconnected graphs -- 3.9 Vertex-magic injections -- 4 Totally Magic Labelings -- 4.1 Basic ideas -- 4.2 Isolates and stars -- 4.3 Forbidden configurations -- 4.4 Unions of triangles -- 4.5 Small graphs -- 4.6 Totally magic injections -- Notes on the Research Problems -- References -- Answers to Selected Exercises.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780817642525
    Language: English
    DOI: 10.1007/978-1-4612-0123-6
    URL: http://dx.doi.org/10.1007/978-1-4612-0123-6
    URL: Volltext
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    Online Resource
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    HU Berlin
    BTU Cottbus
  • 2
    Online Resource
    Online Resource
    Magic Graphs (2001)
    Boston, MA : Birkhäuser
    Details
    UID:
    gbv_1655005189
    Format: Online-Ressource (XIV, 146 p, online resource)
    ISBN: 9781461201236
    Series Statement: SpringerLink
    Content: This book is a good guide for graduate students beginning research in graph labelings. They can see how new mathematics comes into existence. … Throughout the text there are exercises and research problems. … Some are quite easy, some ask the reader to do a complete search for labelings of a particular graph or labelings of a particular type, a few are quite difficult. … The book is a beautiful collection of recent results on the topic of “magic labelings”. -Mathematical Reviews (Review of First Edition) The introductory chapter covers briefly the basics of graph theory and introduces various kinds of magic labelings of graphs. The main three chapters that follow are devoted to the three main types of magic labelings: edge-magic, vertex-magic, and totally magic labellings, respectively. … Not many mathematical prerequisites are needed to read this book although the reader should have some mathematical maturity. -Zentralblatt MATH (Review of First Edition) Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of “magic” ideas have been applied to graphs. Recently there has been a resurgence of interest in “magic labelings” due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include: · a new chapter on magic labeling of directed graphs · applications of theorems from graph theory and interesting counting arguments · new research problems and exercises covering a range of difficulties · a fully updated bibliography and index This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher
    Additional Edition: ISBN 9780817642525
    Additional Edition: Erscheint auch als Druck-Ausgabe Wallis, Walter D., 1941 - Magic graphs Boston : Birkhäuser, 2001 ISBN 0817642528
    Additional Edition: ISBN 3764342528
    Language: English
    Subjects: Mathematics
    RVK:
    SK 890
    Keywords: Graphmarkierung
    DOI: 10.1007/978-1-4612-0123-6
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    URL: Inhaltstext
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    Online Resource
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    UB Potsdam
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