• MAXIMUM INDEPENDENT SET COVER PEBBLING NUMBER OF A STAR

Abstract

A pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. A graph is said to be cover pebbled if every vertex has a pebble on it after a sequence of pebbling moves. The cover pebbling number (G) of a graph G is the minimum number of pebbles that must be placed on the vertices of G such that after a sequence of pebbling moves the graph can be cover pebbled no matter how the pebbles are initially placed on the vertices of the graph G. The maximum independent set cover pebbling number, (G), of a graph G is the minimum number of pebbles that are placed on V(G) such that after a sequence of pebbling moves along a random walk, the set of vertices with pebbles forms a maximum independent set of G, regardless of their initial configuration. In this paper, we determine the maximum independent set cover pebbling number of a star.