Abstract
A pebbling move refers to the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given an initial distribution of pebbles, use pebbling moves to reach a specified goal vertex called the root. The pebbling number of a graph \(\pi (G)\) is the minimum number of pebbles needed so every distribution of \(\pi (G)\) pebbles can reach every choice of the root. We introduce a new variant of graph pebbling, a game between two players. One player aims to move a pebble to the root and the other player aims to prevent this. We show configurations of various classes of graphs for which each player has a winning strategy. We will characterize the winning player for a specific class of diameter two graphs.
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