Abstract
In this article, we study the degree-based topological indices in a random polyomino chain. The key purpose of this manuscript is to obtain the asymptotic distribution, expected value and variance for the degree-based topological indices in a random polyomino chain by using a martingale approach. Consequently, we compute the degree-based topological indices in a polyomino chain, hence some known results from the existing literature about polyomino chains are obtained as corollaries. Also, in order to apply the results, we obtain the expected value of several degree-based topological indices such as Sombor, Forgotten, Zagreb, atom-bond-connectivity, Randić and geometric-arithmetic index of a random polyomino chain.
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