t-CF PEBBLING NUMBER OF SOME STANDARD GRAPHS

Abstract

Graph pebbling is a mathematical process involving the movement of pebbles on a connected graph G according to specific rules. Assume G is a graph with some pebbles distributed over its vertices. A CF pebbling move is defined as the removal of x pebbles from one vertex, followed by discarding  pebbles and moving the remaining  pebbles to an adjacent vertex. The t-CF pebbling number, λ_t(G), of a connected graph G, is the least positive integer n such that any distribution of n pebbles on G allows t pebbles to be carried to any arbitrary vertex using a sequence of CF pebbling moves. In this study, we determine the t-CF pebbling number of path graph, star graph, complete graph and fan graph.