The 2-pebbling property of squares of paths and Graham’s conjecture

Abstract

A pebbling move on a graph G consists of taking two pebbles off one vertex and placing one pebble on an adjacent vertex. The pebbling number of a connected graph G, denoted by f(G), is the least n such that any distribution of n pebbles on G allows one pebble to be moved to any specified vertex by a sequence of pebbling moves. In this paper, we determine the 2-pebbling property of squares of paths and Graham’s conjecture on P2n2$\begin{array}{} P_{2n}^2 \end{array} $.

Keywords

• square of paths
• pebbling number
• pebbling move
• 05c70