Pebbling on some braid graphs

Abstract

Given a distribution of pebbles on the vertices of a connected graph, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The pebbling number, f(G) of a connected graph G, is the smallest positive integer such that from every placement of f(G) pebbles, we can move a pebble to any specified vertex by a sequence of pebbling moves. In this paper, we find the pebbling number for some braid graphs.