TY - JOUR JF - khu-mmr JO - mmr VL - 8 IS - 4 PY - 2022 Y1 - 2022/12/01 TI - Some Properties of the Nil-Graphs of Ideals of Commutative Rings TT - نتایجی پیرامون گراف‌های پوچ وابسته به ایده‌آل‌های یک حلقه جابه‌جایی 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. SP - 238 EP - 255 AU - Nikandish, Reza AD - KW - Nil-graph KW - Complete graph KW - Bipartite graph KW - Genus KW - Independence number UR - http://mmr.khu.ac.ir/article-1-3071-en.html ER -