On Weakly <i>S</i> -Prime Ideal Graph Of a Finite Commutative Ring
Let โ be a finite commutative ring with unity. Let โ be a proper ideal of โ and ๐ฎ is the multiplicative closed subset of โ which is disjoint with โ. The weakly &lt;i&gt;S&lt;/i&gt;-prime ideal graph denoted by G&lt;sub&gt;โ&lt;/sub&gt;(โ) is the undirected graph whose vertex set is the set of elements ๐ข of โ such that the non-zero product ef is in โ and either se is in โ or sf is in โ for some f in โ and the two distinct vertices ๐ข and ๐ฃ are connected by an edge if and only if either se is in โ or sf is in โ for some s in ๐ฎ. The purpose of this article is to investigate the graph theoretic properties of the weakly &lt;i&gt;S&lt;/i&gt;-prime ideal graph associated with โ. This study focuses on rings of order 2๐ญ, 3๐ญ and ๐ญ๐ฎ, where ๐ญ and ๐ฎ are distinct primes. For these rings, the weakly &lt;i&gt;S&lt;/i&gt;-prime ideal graph is a special type of graph and it is explained with examples. Furthermore, the graph theoretic concept of the weakly &lt;i&gt;S&lt;/i&gt;-prime ideal graph G&lt;sub&gt;โ&lt;/sub&gt;(โ) namely its girth, diameter, radius and size are studied. The relation between the weakly &lt;i&gt;S&lt;/i&gt;-prime ideal graph and annihilator ideal graph associated with a ring of order 2๐ญ is described and it is proved that these two graphs are isomorphic.
Authors
- Vasuki Shanmugam
- Kalamani Duraisamy (ORCID: https://orcid.org/0009-0007-7974-5265)
Institutions
- Bharathiar University (IN)
Publication Details
- Journal
- Applied and Computational Mathematics
- Published
- 2026-04-24
- DOI
- https://doi.org/10.11648/j.acm.20261502.12
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 0.00