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Graph Neural Networks (GNNs) have achieved tremendous success in many graph mining tasks benefitting from the message passing strategy that fuses the local structure and node features for better graph representation learning. Despite the success of GNNs, and similar to other types of deep neural networks, GNNs are found to be vulnerable to unnoticeable perturbations on both graph structure and node features. Many adversarial attacks have been proposed to disclose the fragility of GNNs under different perturbation strategies to create adversarial examples. However, vulnerability of GNNs to successful backdoor attacks was only shown recently. In this paper, we disclose the TRAP attack, a Transferable GRAPh backdoor attack. The core attack principle is to poison the training dataset with perturbation-based triggers that can lead to an effective and transferable backdoor attack. The perturbation trigger for a graph is generated by performing the perturbation actions on the graph structure via a gradient based score matrix from a surrogate model. Compared with prior works, TRAP attack is different in several ways: i) it exploits a surrogate Graph Convolutional Network (GCN) model to generate perturbation triggers for a blackbox based backdoor attack; ii) it generates sample-specific perturbation triggers which do not have a fixed pattern; and iii) the attack transfers, for the first time in the context of GNNs, to different GNN models when trained with the forged poisoned training dataset. Through extensive evaluations on four real-world datasets, we demonstrate the effectiveness of the TRAP attack to build transferable backdoors in four different popular GNNs using four real-world datasets.