More on graph pebbling number

Let $G=(V,E)$ be a simple graph. A function φ:V→ N∪ \0\ is called a configuration of pebbles on the vertices of G and the quantity ∑u∈ Vφ(u) is called the size of φ which is just the total number of pebbles assigned to vertices. A pebbling step from a vertex u to one of its neighbors v reduces φ(u) by two and increases φ(v) by one. Given a specified target vertex r we say that φ is t-fold r-solvable, if some sequence of pebbling steps places at least t pebbles on r. Conversely, if no such steps exist, then φ is r-unsolvable. The minimum positive integer m such that every configuration of size m on the vertices of G is t-fold r-solvable is denoted by πₜ(G,r). The t-fold pebbling number of G is defined to be πₜ(G)= maxr∈ V(G)πₜ(G,r). When $t=1$, we simply write π(G), which is the pebbling number of G. In this note, we study the pebbling number for some specific graphs. Also we investigate the pebbling number of corona and neighbourhood corona of two graphs.