Metric dimension in a prime ideal sum graph of a commutative ring

2023/03/10 by M. Adlifard, Adlifard, M., Sh. Niknejad +3
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Graph Labeling and Dimension Problems #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2303.05931

openalex publication_date 2023/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The prime ideal sum graph of a commutative unital ring R, denoted by PIS(R), is an undirect and simple graph whose vertices are non-trivial ideals of R and there exists and edge between to distinct vertices if and only if their sum is a prime ideal of R. In this paper, the metric dimension of PIS(R) is discussed and some formulae for this parameter in PIS(R) are given.

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