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http://hdl.handle.net/10603/15716
Title: | Pebbling and Related Concepts in Graphs |
Researcher: | Samuel Jeyaseelan, S |
Guide(s): | Lourdusamy, A |
Keywords: | adjacent vertex desired vertex Graphs Pebbling Related Concepts vertices of an n-cube |
Upload Date: | 6-Feb-2014 |
University: | Manonmaniam Sundaranar University |
Completed Date: | December 2010 |
Abstract: | Suppose 2n pebbles are arbitrarily placed newlineon the vertices of an n-cube. Does there exist a method that allows us to newlinemake a sequence of moves, each move taking two pebbles off one vertex and newlineplacing one pebble on an adjacent vertex, in such a way that we can end newlineup with a pebble on any desired vertex? This question is answered in the newlineaffirmative by Chung [3]. Pebbling was first introduced into the literature by newlineChung [3]. newlineGiven a graph G, distribute k pebbles (indistinguishable markers) on its newlinevertices in some configuration C. Specifically, a configuration on a graph G is newlinea function from V (G) to N [ {0} representing an arrangement of pebbles on newlineG. For our purposes, we will always assume that G is connected. A pebbling newlinemove is defined as the removal of two pebbles from some vertex and the newlineplacement of one of these pebbles on an adjacent vertex. The pebbling newlinenumber of a connected graph G is the smallest number f(G) such that, newlinehowever f(G) pebbles are distributed on the vertices of G, we can move a newlinepebble to any root vertex by a sequence of pebbling moves [3]. Implicit in this newlinedefinition is the fact that if after moving to vertex v one desires to move to newlineanother root vertex, the pebbles reset to their original initial configuration. newline |
Pagination: | xiii, 154p. |
URI: | http://hdl.handle.net/10603/15716 |
Appears in Departments: | St. Xavier's College |
Files in This Item:
File | Description | Size | Format | |
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01_titles.pdf | Attached File | 27.12 kB | Adobe PDF | View/Open |
02_certificate.pdf | 13.94 kB | Adobe PDF | View/Open | |
03_declaration.pdf | 11.79 kB | Adobe PDF | View/Open | |
04_akcnowledgement.pdf | 18.03 kB | Adobe PDF | View/Open | |
05_preface.pdf | 46.9 kB | Adobe PDF | View/Open | |
06_contents.pdf | 27.17 kB | Adobe PDF | View/Open | |
07_list of figures.pdf | 12.46 kB | Adobe PDF | View/Open | |
08_chapter 1.pdf | 82.4 kB | Adobe PDF | View/Open | |
09_chapter 2.pdf | 279.15 kB | Adobe PDF | View/Open | |
10_chapter 3.pdf | 167.71 kB | Adobe PDF | View/Open | |
11_chapter 4.pdf | 105.77 kB | Adobe PDF | View/Open | |
12_chapter 5.pdf | 102.42 kB | Adobe PDF | View/Open | |
13_chapter 6.pdf | 202.9 kB | Adobe PDF | View/Open | |
14_conclusion.pdf | 36.93 kB | Adobe PDF | View/Open |
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