پیوندهای مفید
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 399 |
| تعداد مقالات | 3,523 |
| تعداد مشاهده مقاله | 5,417,143 |
| تعداد دریافت فایل اصل مقاله | 3,702,970 |
Some results on domination in annihilating-ideal graphs of commutative rings | ||
| Journal of Hyperstructures | ||
| دوره 14، شماره 1، 2025، صفحه 47-56 اصل مقاله (1.6 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.15681.1039 | ||
| نویسنده | ||
| Reza Taheri* | ||
| Department of Mathematics, Shahrekord Branch, Islamic Azad Univercsity, Shahrekord, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Keywords: Annihilating-ideal؛ dominating set؛ domination number؛ total dominating set؛ semi-total dominating set | ||
| مراجع | ||
|
[1] G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr and F. Shahsavari, Minimal prime ideals and cycles in annihilating-ideal graphs, Rocky Mountain J. Math., 5 (2013), 1415-1425. [2] G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr and F. Shahsavari,On the coloring of the annihilating-ideal graph of a commutative ring, Discrete Math., 312 (2012), 2620-2626. [3] G. Aalipour, S. Akbari, M. Behboodi, R. Nikandish and M. J. Nikmehr and F. Shahsavari, The classification of the annihilating-ideal graph of a commutative ring, Algebra Colloquium, 21 (2014), 249-256. [4] F. Aliniaeifard and M. Behboodi,Rings whose annihilating-ideal graphs have positive genus, J. Algebra Appl., 11, 1250049 (2012), [13 pages]. [5] F. Aliniaeifard, M. Behboodi, E. Mehdi-Nezhad and A. M. Rahimi, The annihilating-ideal graph of a commutative ring with respect to an ideal, Commun. Algebra, 42 (2014), 2269-2284. [6] F. Aliniaeifard, M. Behboodi, E. Mehdi-Nezhad and A. M. Rahimi, The annihilating-ideal graph of a commutative ring with respect to an ideal, Communication in Algebra, 42(5) (2014), 2269-2284. [7] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra, 320 (2008), 2706-2719. [8] D. F. Anderson and P. S. Livingston,The zero-divisor graph of a commutative ring, J. Algebra, 217 (1999), 434-447. 10 R. Taheri [9] M. F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, London, 1969. [10] I. Beak, Coloring of commutative rings, J. Algebra, 116(1) (1988), 208-266. [11] M. Behboodi,Zero divisor graphs for modules over commutative rings, J. Commut. Algebra, 4 (2012), 175-197. [12] M. Behboodi, Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl., 10 (2011), 727-739. [13] M. Behboodi, Z. Rakeei,The annihilating-ideal graph of commutative rings II, J. Algebra Appl., 10 (2011) 740-753. [14] I. Chakrabarty, S. Ghosh, T. K. Mukherjee and M. K. Sen, Intersection graphs of ideals of rings, Discrete Math., 309 (2009), 5381-5392. [15] S. Kiani, H. R. Maimani and R. Nikandish,Some Results On the Domination Number of a Zero-divisor Graph, Canad. Math. Bull. Vol., 57(3) (2014), 573-578. [16] R. Nikandish and H.R. Maimani,Dominatig sets of the annihilating-ideal graphs, Electronic Notes Discrete Math., 45 (2014), 17.22. [17] S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra, 31(9) (2003), 4425-4443. [18] R. Y. Sharp, Steps in Commutative Algebra, 2nd end., London Mathematical Society Student Texts, Vol. 51 (cambridge University Press, Cambridge, 1990). [19] R. Taheri, M. Behboodi and A. Tehranian, The spectrum subgraph of the annihilating-ideal graph of a commutative ring, J. Algebra Appl., 14 (2015) . [20] R. Taheri, A. Tehranian, The principal ideal subgraph of the annihilating-ideal graph of commutative rings, J. Algebra structures Appl., 3(1) (2016), 39-52. | ||
|
آمار تعداد مشاهده مقاله: 61 تعداد دریافت فایل اصل مقاله: 293 |
||