  In this paper, we study topological indices in random spiro chains via a
martingale approach. In which their explicit analytical expressions of the
exact distribution, expected value and variance are obtained. As n goes to
infinity, the asymptotic normality of topological indices of a random spiro
chain is established through the Martingale Central Limit Theorem. In
particular, we compute the Nirmala, Sombor, Randic and Zagreb index for a
random spiro chain along with their comparative analysis.
