This paper investigates tilings of a \(2 \times n\) rectangle using vertical and horizontal dominos. It is well-known that these tilings are counted by the Fibonacci numbers. We associate a graph to each tiling by converting the corners and borders of the dominos to vertices and edges. We study the combinatorial, probabilistic, and graph-theoretic properties of the resulting “domino tiling graphs.” In particular, we prove central limit theorems for naturally occurring statistics on these graphs. Some of these results are then extended to more general tiling graphs.
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