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

Jamsheena, P.; Chithra, A. V.

doi:10.22108/toc.2025.141755.2182

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	Metric dimension and Zagreb indices of essential ideal graph of a finite commutative ring
Transactions on Combinatorics
دوره 15، شماره 2، شهریور 2026، صفحه 91-110 اصل مقاله (546.6 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.141755.2182
نویسندگان
P. Jamsheena^* ¹؛ A. V. Chithra²
¹PG and Research Department of Mathematics, Farook College, P.O. Farook College, Kozhikode, Kerala, India- 673632
²Department of Mathematics, National Institute of Technology Calicut, Kozhikode, 673601, Kerala, India
چکیده
Let $R$ be a commutative ring with unity. The essential ideal graph $\mathcal{E}_{R}$ of $R$ is a graph whose set of vertex consists of all nonzero proper ideals of R. Two vertices $\hat{I}$ and $\hat{J}$ are adjacent if and only if $\hat{I}+ \hat{J}$ is an essential ideal. In this paper, we characterize the graph $\mathcal{E}_{R}$ as having a finite metric dimension. Furthermore, we identify that the essential ideal graph and the annihilating ideal graph of the ring $\mathbb{Z}_{n}$ are isomorphic whenever $n$ is a product of distinct primes. In addition, we estimate the metric dimension of the essential ideal graph of the ring $\mathbb{Z}_{n}$. Moreover, we determine the topological indices, namely the first and second Zagreb indices, of $\mathcal{E}_{\mathbb Z_n}$.
کلیدواژه‌ها
Essential ideal graph؛ metric dimension؛ first and second Zagreb indices

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