%0 Journal Article %A Nikandish, Reza %T Some Properties of the Nil-Graphs of Ideals of Commutative Rings %J Mathematical Researches %V 8 %N 4 %U http://mmr.khu.ac.ir/article-1-3071-en.html %R %D 2022 %K Nil-graph, Complete graph, Bipartite graph, Genus, Independence number, %X 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. %> http://mmr.khu.ac.ir/article-1-3071-en.pdf %P 238-255 %& 238 %! %9 Original Manuscript %L A-10-1190-1 %+ %G eng %@ 2588-2546 %[ 2022