intersection graph of amalgamated algebras along an ideal

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).