On the Sombor index of the total graph and the unit graph of commutative rings

In this paper, we investigate the Sombor index of the total graph and unit graph of Zₙ which is denoted by T_ (Zₙ) and G (Zₙ) respectively for n \2k, p^{, pq, p²q\} where p and q are distinct odd prime numbers such that p < q. Moreover, we compute the Sombor index of any finite local ring.