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.

甲打狗移动指的是从一个顶点去除两个卵石和放置一个卵石在相邻顶点的动作。图的研磨目标是：给定卵石的初始分布，使用研磨动作来达到指定的目标顶点，称为root。的pebbling数的曲线图的\（\ PI（G）\）是必须的，从而每一个分配卵石的最小数目\（\ PI（G）\）卵石可以触及根的每一个选择。我们引入了图争夺的新变体，这是两个玩家之间的游戏。一个玩家旨在将小卵石移至根部，而另一个玩家旨在防止这种情况。我们展示了每种玩家都有获胜策略的各种图表的配置。我们将针对特定类别的直径两张图表来描述获胜玩家的特征。