COVER PEBBLING CYCLES AND CERTAIN GRAPH PRODUCTS

MAGGY TOMOVA AND CINDY WYELSAbstract. A pebbling step on a graph consists of removing two pebbles fromone vertex and placing one pebble on an adjacent vertex. A graph is said to becover pebbled if every vertex has a pebble on it after a series of pebbling steps.The cover pebbling number of a graph is the minimum number of pebbles suchthat the graph can be cover pebbled, no matter how the pebbles are initiallyplaced on the vertices of the graph. In this paper we determine the coverpebbling numbers of cycles, finite products of paths and cycles, and productsof a path or a cycle with good graphs, amongst which are trees and completegraphs. In the process we provide evidence in support of an affirmative answerto a question posed in a paper by Cundiff, Crull, et al.2000 AMS Subject Classification: 05C99, 05C38Keywords: graph pebbling; cover pebbling; Graham’s conjecture; cycles.