The 2-Pebbling Property of the Middle Graph of Fan Graphs

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 but arbitrary vertex by a sequence of pebbling moves. This paper determines the pebbling numbers and the 2-pebbling property of the middle graph of fan graphs.