Metric Dimension and Zagreb indices of Essential Ideal Graph of a finite Commutative Ring

	Metric Dimension and Zagreb indices of Essential Ideal Graph of a finite Commutative Ring
Transactions on Combinatorics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 اردیبهشت 1404
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.141755.2182
نویسندگان
Jamsheena P^* ؛ Chithra A V
Department 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 \textit{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

آمار تعداد مشاهده مقاله: 19

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