On Weakly S -Prime Ideal Graph Of a Finite Commutative Ring
Year: 2026
Type: article
Abstract: Let ā be a finite commutative ring with unity. Let ā be a proper ideal of ā and š® is the multiplicative closed subset of ā which is disjoint with ā. The weakly S-prime ideal graph denoted by Gā(ā) is the undirected graph whose vertex set is the set of elements š¢ of ā such that the non-zero product ef is in ā and either se is in ā or sf is in ā for some f in ā and the two distinct vertices š¢ and š£ are connected by an edge if and only if either se is in ā or sf is in ā for some s in š®. The purpose of this article is to investigate the graph theoretic properties of the weakly S-prime ideal graph associated with ā. This study focuses on rings of order 2š, 3š and šš®, where š and š® are distinct primes. For these rings, the weakly S-prime ideal graph is a special type of graph and it is explained with examples. Furthermore, the graph theoretic concept of the weakly S-prime ideal graph Gā(ā) namely its girth, diameter, radius and size are studied. The relation between the weakly S-prime ideal graph and annihilator ideal graph associated with a ring of order 2š is described and it is proved that these two graphs are isomorphic.
Authors: Kalamani Duraisamy, Vasuki Shanmugam
Institution: Bharathiar University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7160184526