Cover pebbling numbers and bounds for certain families of graphs

Details Cover pebbling numbers and bounds for certain families of graphs Cover pebbling numbers and bounds for certain families of graphs

2004-09-18

arxiv.org/abs/math/0409321v1

Mathematics

Combinatorics

10 pages, 1 figure, submitted to Discrete Mathematics

Scientific paper

Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph, gamma(G), is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are initially distributed. The cover pebbling number for complete multipartite graphs and wheel graphs is determined. We also prove a sharp bound for gamma(G) given the diameter and number of vertices of G.

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