NON-NILPOTENT GRAPH OF COMMUTATIVE RINGS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 149-162 اصل مقاله (163.04 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12064.1620 | ||
| نویسندگان | ||
| Hussain Mohammed Imdadul Hoque1؛ Helen Kumari Saikia1؛ Jituparna Goswami* 2؛ Diksha Patwari1 | ||
| 1Department of Mathematics, Gauhati University, Guwahati-781014, India. | ||
| 2Department of Mathematics, Gauhati University, Guwahati-14, Assam, India. | ||
| چکیده | ||
| Let R be a commutative ring with unity. Let Nil(R) be the set of all nilpotent elements of R and Nil(R) = R \ Nil(R) be the set of all non-nilpotent elements of R. The non-nilpotent graph of R is a simple undirected graph GNN(R) with Nil(R) as vertex set and any two distinct vertices x and y are adjacent if and only if x+y ∈ Nil(R). In this paper, we introduce and discuss the basic properties of the graph GNN(R). We also study the diameter and girth of GNN(R). Further, we determine the domination number and the bondage number of GNN(R). We establish a relation between diameter and domination number of GNN(R). We also establish a relation between girth and bondage number of GNN(R). | ||
| کلیدواژهها | ||
| Commutative rings؛ Non-nilpotent graph؛ Nilpotent elements, Non-nilpotent elements | ||
| مراجع | ||
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