Driver vigilance detection is an important topic for traffic safety improvement and brain-computer interface design. Electroencephalography (EEG) can directly provide real-time information and is sensitive to the change of vigilance. Thus, EEG signals are widely used for driver vigilance detection. Previous studies commonly acquired EEG signals from a large number of electrode channels and utilized all the collected data for recognition tasks, which may introduce a large amount of noise and redundant data and limit their application potentials in practical systems. This paper examines the potential of using EEG signals from only one frequency band or from only a small subset of related electrode channels in recognizing driver vigilance state. The widely used SEED VIG dataset is adopt for experiments. Four candidate sets of EEG frequency bands and four candidate sets of EEG electrode channels are determined according to the statistical significance results of EEG power spectral density (PSD) features and differential entropy (DE) features. The experimental results show that the recognition accuracy is higher when using EEG signals from the selected frequency band (i.e., alpha band) or the selected electrodes (i.e., T7, TP7, CP1) than when using all the data. Specifically, the best recognition accuracy is 91.31% for the alpha band and 76.81% for the selected electrodes. These results indicate that higher driver vigilance recognition accuracy can be achieved with much less amount of data, which would facilitate the development of wearable equipment based on EEG signals.