Cover pebbling numbers and bounds for certain families of graphs

Abstract

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.

10 pages, 1 figure, submitted to Discrete Mathematics

References in corpus (2)

• A Survey of Graph Pebbling
• Conditions for Weighted Cover Pebbling of Graphs

Cited by in corpus (7)

• Recent Progress in Graph Pebbling
• An application of graph pebbling to zero-sum sequences in abelian groups
• Sierpi\' nski Gasket Graphs and Some of Their Properties
• The Complexity of Pebbling and Cover Pebbling
• Domination Cover Pebbling: Structural Results
• Threshold and Complexity Results for the Cover Pebbling Game
• The Pi-Pebbling Function