The domination cover pebbling number of the square of a path

Abstract

Given a configuration of pebbles on the vertices of a connected graph GG, 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, ψ(G)ψ(G), of a graph GG is the minimum number of pebbles that have to be placed on V(G)V(G) such that after a sequence of pebbling moves, the set of vertices with pebbles forms a dominating set of GG, regardless of the initial configuration. In this paper, we determine the domination cover pebbling number for the square of a path.