SUMMARY
Polyomino graphs is one of the research objectives in statistical physics and in modeling problems of surface chemistry. A random polyomino chain is a subgraph of a polyomino graph. The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. In this paper, we characterize the graphs with the extremal matching energy among all random polyomino chains of a polyomino graph by the probability method.