T-CF pebbling number of some path related 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, λt(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 paper, we determine the t-CF pebbling number of paths and path-related graphs, providing insights into the relationship between graph structure and pebbling strategies.