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Some results on domination in annihilating-ideal graphs of commutative rings | ||
| Journal of Hyperstructures | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 اردیبهشت 1404 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 | ||
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