Research On Pebbling Number Of Some Graphs

The origins of graph pebbling reside in combinatorial number theory and group theory. The idea of pebbling was proposed by Lagarias and Saks. The concept was introduced at first time in the paper by Chung. It is a model for the transportation of resources. Starting with a pebble distribution on the vertices of a simple connected graph, a pebbling move removes two pebbles from a vertex and adds one pebble at an adjacent vertex. We can think of the pebbles as fuel containers. Then the loss of the pebble during a move is the cost of transportation. The pebbling number of a graph G, f(G), is the leastn such that, no matter how n pebbles are placed on the vertices of G, one pebble can be moved to any vertex by a sequence of pebbling moves.In this paper, we firstly introduce the background and the development of the graph pebbling. Secondly, based on the previous studies, this paper mainly focuses on the pebbling of gear graph Dn,4 and the more general graph Dn,2m. We compute the pebbling number of gear graph Dn,4, moreover, we compute the pebbling number and others related parameters of the graph Dn,2m. Finally, we prove that Dn.4 satifies 2-pebbling property.