A Graph Pebbling Algorithm on Weighted Graphs
نویسندگان
چکیده
منابع مشابه
A Graph Pebbling Algorithm on Weighted Graphs
A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The pebbling number of a weighted graph is the smallest number m needed to guarante...
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In a graph G with a distribution of pebbles on its vertices, a pebbling move is the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. A weight function on G is a nonnegative integer-valued function on the vertices of G. A distribution of pebbles on G covers a weight function if there exists a sequence of pebbling moves that gives a new distribution in ...
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We say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let kðdÞ denote the least positive integer so that every graph G with diameter at most d and connectivity at least kðdÞ is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must sa...
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We survey results on the pebbling numbers of graphs as well as their historical connection with a number-theoretic question of Erdős and Lemke. We also present new results on two probabilistic pebbling considerations, first the random graph threshold for the property that the pebbling number of a graph equals its number of vertices, and second the pebbling threshold function for various natural...
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Given a distribution of pebbles on the vertices of a graph G, a pebbling move takes two pebbles from one vertex and puts one on a neighboring vertex. The pebbling number Π(G) is the least k such that for every distribution of k pebbles and every vertex r, a pebble can be moved to r. The optimal pebbling number ΠOPT (G) is the least k such that some distribution of k pebbles permits reaching eac...
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ژورنال
عنوان ژورنال: Journal of Graph Algorithms and Applications
سال: 2010
ISSN: 1526-1719
DOI: 10.7155/jgaa.00205