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Graceful Labelings of Infinite Graphs: (English)

Graceful Labelings of Infinite Graphs: (English)

          
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About the Book

This dissertation, "Graceful Labelings of Infinite Graphs" by Tsz-lung, Chan, 陳子龍, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled GRACEFUL LABELINGS OF INFINITE GRAPHS submitted by CHAN Tsz Lung for the Degree of Master of Philosophy at The University of Hong Kong in August 2007 Graph labeling involves the assignment of integers to vertices or edges, or both, subject to certain conditions. Not only does it become an active area of research, graph labeling also finds applications in graph decomposition, ne- ofield, topological graph theory, coding theory, radio channel assignment and network addressing. A graceful labeling of a graph G with n edges is an injective function from the set of vertices of G to the set {0,1,2, ..., n} such that the edge labels, the absolute difference between the two endvertex labels, are all distinct. One of themostfamousopenproblemsingraphtheoryistheGracefulTreeConjecture which states that every finite tree has a graceful labeling. Despite forty years of research effort, little progress has been made. Today, some of the known grace- ful trees are caterpillars, trees with at most 4 endvertices, trees with diameter at most 5, and trees with at most 27 vertices. Previous works on graceful labeling focused on finite graphs only. In this thesis, graceful labelings of infinite graphs were investigated in some depths. First, the notions of bijective graceful N-labeling and bijective graceful N/N- labeling of infinite graphs were introduced. Such labelings were then shown to be possible for infinite graphs built by certain types of graph amalgamations. Finally, based on the tools developed, all infinite trees having a bijective grace-ful N/N-labeling were characterized. This, in turn, solved the Graceful Tree Conjecture for infinite trees. DOI: 10.5353/th_b3933218 Subjects: Graph labelings


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Product Details
  • ISBN-13: 9781361479582
  • Publisher: Open Dissertation Press
  • Publisher Imprint: Open Dissertation Press
  • Height: 279 mm
  • No of Pages: 42
  • Spine Width: 6 mm
  • Width: 216 mm
  • ISBN-10: 1361479582
  • Publisher Date: 27 Jan 2017
  • Binding: Hardback
  • Language: English
  • Series Title: English
  • Weight: 399 gr


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