Recently, the emerging graph Transformers have made significant advancements for node classification on graphs. In most graph Transformers, a crucial step involves transforming the input graph into token sequences as the model input, enabling Transformer to effectively learn the node representations. However, we observe that existing methods only express partial graph information of nodes through single-type token generation. Consequently, they require tailored strategies to encode additional graph-specific features into the Transformer to ensure the quality of node representation learning, limiting the model flexibility to handle diverse graphs. To this end, we propose a new graph Transformer called NTFormer to address this issue. NTFormer introduces a novel token generator called Node2Par, which constructs various token sequences using different token elements for each node. This flexibility allows Node2Par to generate valuable token sequences from different perspectives, ensuring comprehensive expression of rich graph features. Benefiting from the merits of Node2Par, NTFormer only leverages a Transformer-based backbone without graph-specific modifications to learn node representations, eliminating the need for graph-specific modifications. Extensive experiments conducted on various benchmark datasets containing homophily and heterophily graphs with different scales demonstrate the superiority of NTFormer over representative graph Transformers and graph neural networks for node classification.