DefinePK

Abstract

Given a configuration of pebbles on the vertices of a connected graph \(G\), a pebbling move (or pebbling step) is defined as the removal of two pebbles from a vertex and placing one pebble on an adjacent vertex. The domination cover pebbling number, \(\psi(G)\), of a graph \(G\) is the minimum number of pebbles that have to be placed on \(V (G)\) such that after a sequence of pebbling moves, the set of vertices with pebbles forms a dominating set of \(G\), regardless of the initial configuration. In this paper, we determine the domination cover pebbling number for the square of a path.