Intersection graph of amalgamated algebras along an ideal

Document Type : Research Paper

Authors

1 Department of Mathematics, ET.C., Islamic Azad University, Tehran, Iran

2 Department of Mathematics, SR.C., Islamic Azad University, Tehran, Iran

Abstract

Let f:R→S be a ring homomorphism of commutative rings with identity, and let J be a non-zero proper ideal of S. The amalgamation of R with S along J with respect to f denoted by R∝fJ, was introduced by D'Anna et al. in 2010. In this paper, we investigate some properties of the intersection graph of ideals of R∝fJ. We show that Γ(R∝fJ) is always connected and diam(Γ(R∝fJ))≤2. We obtain some conditions which implies that for an integer n >0, K_{n} is a subgraph of Γ(R∝fJ). We show that if R is a local ring, and J⊆Jac(S), where Jac(S) is the Jacobson radical of S, then Γ(R∝fJ) is planar if and only if Γ(R∝fJ) is star graph or K3 or K4, provided under certain conditions. Finally, we study the dominating number of Γ(R∝fJ).

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References

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Journal of Hyperstructures
Volume 15, Issue 1
June 2026
Pages 24-33

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