To address the issue of weak transient zero-sequence current features and noise interference in single-phase high-resistance grounding faults in arc suppression coil grounded systems, this paper proposes a fault line selection method based on Variational Mode Decomposition (VMD) and weighted graph smoothness. VMD is used to decompose the half-cycle post-fault zero-sequence current of each feeder into several Intrinsic Mode Functions (IMFs). A graph is constructed for each IMF, and the normalized graph Laplacian quadratic form is computed as the graph smoothness measure, highlighting the fluctuation intensity of the IMF waveforms of the faulty line. Then, the energy proportion of each IMF is used as a weight to construct the weighted graph smoothness for each feeder, adaptively emphasizing low-frequency fault features of the IMFs while suppressing high-frequency noise interference. After normalization, the weighted graph smoothness of each line is compared with the sum of those of the remaining lines, establishing criteria for line faults and bus faults without requiring a manually set threshold. Simulation results show that the proposed method accurately identifies the faulty line under various conditions, including different transition resistances, strong noise, various fault inception angles, and fault locations, demonstrating good robustness and adaptability.