TY - JOUR T1 - Some Properties of the Nil-Graphs of Ideals of Commutative Rings TT - نتایجی پیرامون گراف‌های پوچ وابسته به ایده‌آل‌های یک حلقه جابه‌جایی JF - khu-mmr JO - khu-mmr VL - 8 IS - 4 UR - http://mmr.khu.ac.ir/article-1-3071-en.html Y1 - 2022 SP - 238 EP - 255 KW - Nil-graph KW - Complete graph KW - Bipartite graph KW - Genus KW - Independence number N2 - Let R be a commutative ring with identity and Nil(R) be the set of nilpotent elements of R. The nil-graph of ideals of R is defined as the graph AG_N(R) whose vertex set is {I:(0)and there exists a non-trivial ideal such that and two distinct vertices and are adjacent if and only if . Here, we study conditions under which is complete or bipartite. Also, the independence number of is determined, where is a reduced ring. Finally, we classify Artinian rings whose nil-graphs of ideals have genus at most one. M3 ER -