Author | Wallis, W. D. author |
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Title | Magic Graphs [electronic resource] / by W. D. Wallis |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0123-6 |
Descript | XIV, 146 p. online resource |
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