| Summary: | Let S=ℤℊ3×ℤI1I2 be a commutative ring where ℊ,I1 and I2 are positive prime integers with I1≠I2. The zero-divisor graph assigned to S is an undirected graph, denoted as YS with vertex set V(Y(S)) consisting of all Zero-divisor of the ring S and for any c, d ∈V(Y (S)), cd∈EYS if and only if cd =0. A topological index/descriptor is described as a topological-invariant quantity that transforms a molecular graph into a mathematical real number. In this paper, we have computed distance-based polynomials of YR i-e Hosoya polynomial, Harary polynomial, and the topological indices related to these polynomials namely Wiener index, and Hyper-Wiener index.
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