Metric dimension and Zagreb indices of essential ideal graph of a finite commutative ring

Let R be a commutative ring with unity. The essential ideal graph ER of R is a graph whose vertex set consists of all nonzero proper ideals of R. Two vertices Î and Ĵ are adjacent if and only if Î+ Ĵ is an essential ideal. In this paper, we characterize the graph ER as having a finite metric dimension. Additionally, we identify that the essential ideal graph and annihilating ideal graph of the ring Zₙ are isomorphic whenever n is a product of distinct primes. Also, we estimate the metric dimension of the essential ideal graph of the ring Zₙ. Furthermore, we determine the topological indices, namely the first and the second Zagreb indices, of EZₙ.