2-restricted optimal pebbling number of some dendrimers

This paper studies the 2-restricted optimal pebbling number of certain dendrimer graphs. in graph pebbling, a configuration is a distribution of pebbles on the vertices of a simple connected graph g. a pebbling move removes two pebbles from a vertex and places one on an adjacent vertex. a t-restricted pebbling configuration (trpc) is an initial placement where no vertex holds more than t pebbles. a configuration is solvable if, for any target vertex v, a sequence of pebbling moves can place at least one pebble on v. the t-restricted optimal pebbling number, denoted πt*(g), is the minimum number of pebbles required for a solvable trpc on g. we focus on the case t=2 and determine π2*(g) for several classes of dendrimers.