2-Target t-pebbling number of path-derived graphs

Chung introduced the concept of a pebbling move on a graph, which consists of selecting a vertex containing at least two pebbles, removing those two pebbles, and placing one pebble on an adjacent vertex. The 2-target pebbling number of pair of vertices $u,v$ in graph a G, denoted φ(G,u,v) is the minimum number of pebbles such that for any distribution of φ(G,u,v) pebbles on G, it is possible to simultaneously move a pebble to u and v by a sequence of pebbling moves. The 2-target pebbling number of graph G, denoted by φ(G), is the maximum φ(G,u,v) over all pairs of the vertices in G. In this paper, we discuss the 2-target pebbling number for shadow, total, and square graphs of path graph.