منابع مشابه
Pebbling and optimal pebbling in graphs
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...
متن کاملPebbling in Split Graphs
Finding the pebbling number of a graph is harder than NP-complete (Π 2 complete, to be precise). However, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter two graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and ma...
متن کاملPebbling in dense graphs
A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. The pebbling number of a graph G is the minimum number π(G) so that every configuration of π(G) pebbles is solvable. A graph is Class 0 if its pebbling number equals its number of vertices. A function is a pebbling threshold for a sequence of gra...
متن کاملPebbling Graphs of Fixed Diameter
Given a configuration of indistinguishable pebbles on the vertices of a connected graph G on n vertices, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one pebble on an adjacent vertex. The m-pebbling number of a graph G, πm(G), is the smallest integer k such that for each vertex v and each configuration of k pebbles on G there is a sequence of p...
متن کاملCritical Pebbling Numbers of Graphs
We define three new pebbling parameters of a connected graph G, the r-, g-, and ucritical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices n and the diameter d of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the r-critical pebbling number, and distinguish b...
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ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 1994
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita/1994280605571