Analysis of Some Topological Indices Over the Weakly Zero-Divisor Graph of the Ring \(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r\)

In this paper, we study some basic properties of weakly zero-divisor graph of the ring \(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r\) , denoted by \(\text {W}{\Gamma }(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r)\) , where p, q and r are prime numbers greater than 2 and not necessarily distinct. Further, we discuss Wiener index, Gutman index, first K Banhatti index, second K Banhatti index, Forgotten topological index, Forgotten topological coindex, and degree distance index of \(\text {W}{\Gamma }(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r)\) .