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

2024/07/03 by P, Jamsheena, A, Chithra
#05C07 #05C12 #05C25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.02938

Abstract

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

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