A note on pebbling bound for a product of Class 0 graphs

Abstract

Let [Formula: see text] be a connected graph. For a configuration of pebbles on the vertices of [Formula: see text], a pebbling move on [Formula: see text] is the process of taking two pebbles from a vertex and adding one of them on an adjacent vertex. The pebbling number of [Formula: see text], denoted by [Formula: see text], is the least number of pebbles to guarantee that for any configuration of pebbles on [Formula: see text] and arbitrary vertex [Formula: see text], there is a sequence of pebbling movement that places at least one pebble on [Formula: see text]. The graph [Formula: see text] is said to be of Class 0 if its pebbling number equals its order. For a Class [Formula: see text] connected graph [Formula: see text], we improve a recent upper bound for [Formula: see text] in terms of [Formula: see text].