۲-Restricted optimal pebbling number of some dendrimers

This paper studies the ۲-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=۲ and determine π۲*(G) for several classes of dendrimers.

کلیدواژه ها:

Pebbling number ، Optimal pebbling number ، t-restricted optimal pebbling number ، ۲-restricted optimal pebbling confugration