On t-pebbling graphs

Abstract

The t-pebbling number f _t (G) of a graph G, is the least positive integer m such that however m pebbles are placed on the vertices of G, we can move t pebbles to any vertex by a sequence of pebbling moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. In this paper, we compute the t-pebbling number of complete r-partite graphs and we study the generalized Graham's Conjecture f _t(G × H) ≤ f(G)f _t(H) for product of graphs.