Some results on domination in annihilating-ideal graphs of commutative rings
Abstract. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are adjacent if and only if IJ = (0). Let G...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Mohaghegh Ardabili
2025-06-01
|
| Series: | Journal of Hyperstructures |
| Subjects: | |
| Online Access: | https://jhs.uma.ac.ir/article_3813_4ad6268f421b6dcffe7f9d72bf3fa047.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849427787351326720 |
|---|---|
| author | Reza Taheri |
| author_facet | Reza Taheri |
| author_sort | Reza Taheri |
| collection | DOAJ |
| description | Abstract. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are adjacent if and only if IJ = (0). Let G = (V; E) be a graph. A domination set for G is a subset S of V such that every vertex not in S is joined to at least one member of S by some edge. The domination number γ(G) is the minimum cardinality among the dominating sets of G. In this paper, we study and characterize the dominating sets and domination numbers of the annihilating-ideal graph AG(R) for a commutative ring R. |
| format | Article |
| id | doaj-art-ebde4296459948049a3f5ab94b8ddca3 |
| institution | Kabale University |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-ebde4296459948049a3f5ab94b8ddca32025-08-20T03:28:54ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662025-06-01141475610.22098/jhs.2025.15681.10393813Some results on domination in annihilating-ideal graphs of commutative ringsReza Taheri0Department of Mathematics, Shahrekord Branch, Islamic Azad Univercsity, Shahrekord, IranAbstract. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are adjacent if and only if IJ = (0). Let G = (V; E) be a graph. A domination set for G is a subset S of V such that every vertex not in S is joined to at least one member of S by some edge. The domination number γ(G) is the minimum cardinality among the dominating sets of G. In this paper, we study and characterize the dominating sets and domination numbers of the annihilating-ideal graph AG(R) for a commutative ring R.https://jhs.uma.ac.ir/article_3813_4ad6268f421b6dcffe7f9d72bf3fa047.pdfkeywords: annihilating-idealdominating setdomination numbertotal dominating setsemi-total dominating set |
| spellingShingle | Reza Taheri Some results on domination in annihilating-ideal graphs of commutative rings Journal of Hyperstructures keywords: annihilating-ideal dominating set domination number total dominating set semi-total dominating set |
| title | Some results on domination in annihilating-ideal graphs of commutative rings |
| title_full | Some results on domination in annihilating-ideal graphs of commutative rings |
| title_fullStr | Some results on domination in annihilating-ideal graphs of commutative rings |
| title_full_unstemmed | Some results on domination in annihilating-ideal graphs of commutative rings |
| title_short | Some results on domination in annihilating-ideal graphs of commutative rings |
| title_sort | some results on domination in annihilating ideal graphs of commutative rings |
| topic | keywords: annihilating-ideal dominating set domination number total dominating set semi-total dominating set |
| url | https://jhs.uma.ac.ir/article_3813_4ad6268f421b6dcffe7f9d72bf3fa047.pdf |
| work_keys_str_mv | AT rezataheri someresultsondominationinannihilatingidealgraphsofcommutativerings |