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PEBBLING EXPONENTS OF PATHS

A pebbling move on a connected graph G is taking two pebbles ofi of one vertex and placing one of them on an adjacent vertex. For a connected graph G, G p (p > 1) is the graph obtained from G by adding the edges (u;v) to G whenever 2 • dist(u;v) • p in G. And the pebbling exponent of a graph G to be the least power of p such that the pebbling number of G p is equal to the number of vertices of G. We compute the pebbling number of fourth power of paths so that the pebbling exponents of some paths are calculated.