# A survey on the Intersection graphs of ideals of rings

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### "A survey on the Intersection graphs..." refers background in this paper

...For details on terminology and results related to ring theory readers can refer [11, 46, 55, 60, 63, 67, 69] and for information on graph theory readers can refer [51, 68, 101]....

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3,265 citations

### "A survey on the Intersection graphs..." refers background in this paper

...One can refer [53] for various results related to domination parameters....

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1,215 citations

### "A survey on the Intersection graphs..." refers background in this paper

...We know that every non-orientable compact surface is a connected sum of finite copies of projective planes [70]....

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...It is well known that any compact surface is either homeomorphic to a sphere or to a connected sum of g tori or to a connected sum of k projective planes [70]....

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1,087 citations

### "A survey on the Intersection graphs..." refers background in this paper

...Many graphs related to the ring structure [33, 47] such as the zero-divisor graph [2, 3, 10, 81], the total graph and regular graph [1], the annihilating-ideal graph[14, 15], the annihilator-inclusion ideal graph [7], the toroidal annihilating-ideal graph [64], the sum-annihilating essential ideal graph [6] and the comaximal ideal graph [97]....

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982 citations

### Additional excerpts

...It follows from Kuratowski’s Theorem [66] that a graph is planar if and only if it contains no subgraph homeomorphic from the complete graph K5 or from the complete bipartite graph K3,3....

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