منابع مشابه
t-Pebbling Number of Some Multipartite Graphs
Given a configuration of pebbles on the vertices of a graph G, a pebbling move consists of taking two pebbles off some vertex v and putting one of them back on a vertex adjacent to v. A graph is called pebbleable if for each vertex v there is a sequence of pebbling moves that would place at least one pebble on v. The pebbling number of a graph G, is the smallest integer m such that G is pebblea...
متن کاملThe t-Pebbling Number is Eventually Linear in t
In graph pebbling games, one considers a distribution of pebbles on the vertices of a graph, and a pebbling move consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The t-pebbling number πt(G) of a graph G is the smallest m such that for every initial distribution of m pebbles on V (G) and every target vertex x there exists a sequence of pebbling moves leading t...
متن کاملThe Optimal Pebbling Number of the Caterpillar
Let G be a simple graph. If we place p pebbles on the vertices of G, then a pebbling move is taking two pebbles off one vertex and then placing one on an adjacent vertex. The optimal pebbling number of G, f ′(G), is the least positive integer p such that p pebbles are placed suitably on vertices of G and for any target vertex v of G, we can move one pebble to v by a sequence of pebbling moves. ...
متن کاملThe cover pebbling number of graphs
A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling...
متن کاملt-Pebbling and Extensions
We give upper bounds on t-pebbling numbers of graphs of small diameter and investigate the relationships between these results and those relating to fractional pebbling. Furthermore, we present a connection between optimal pebbling and linear optimization and utilize this relationship in analyzing various graphs. We introduce the optimal fractional pebbling number of a graph and provide a combi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.08.024