Khoramdel, MehdiAtani, Shahabaddin EbrahimiPishhesari, Saboura Dolati2021-11-092021-11-092019-08-01https://doi.org/10.31801/cfsuasmas.534944http://hdl.handle.net/20.500.12575/75962In this paper, we introduce and investigate a new graph of a commutative ring R, denoted by G(R), with all nontrivial ideals of R as vertices, and two distinct vertices I and J are adjacent if and only if ann(I∩J)=ann(I)+ann(J). In this article, the basic properties and possible structures of the graph G(R) are studied and investigated as diameter, girth, clique number, cut vertex and domination number. We characterize all rings R for which G(R) is planar, complete and complete r-partite. We show that, if (R,M) is a local Artinian ring, then G(R) is complete if and only if Soc(R) is simple. Also, it is shown that if R is a ring with G(R) is r-regular, then either G(R) is complete or null graph. Moreover, we show that if R is an Artinian ring, then R is a serial ring if and only if G(R/I) is complete for each ideal I of R.enIdealsClique numberComplete r-partiteArticle682228322972618-6470