The covering cover pebbling number for some acyclic graphs

Abstract

The covering cover pebbling number, \(\sigma(G)\), of a graph \(G\), is the smallest number such that some distribution \(D \in \mathscr{K}\) is reachable from every distribution starting with \(\sigma(G)\) (or more) pebbles on \(G\), where \(\mathscr{K}\) is a set of covering distributions. In this paper, we determine the covering cover pebbling number for two families of graphs those do not contain any cycles.