The text files contain all k-vertex-critical (P_5, gem)-free graphs for k=6,7 (k=4,5 can be found here: https://arxiv.org/pdf/2108.05492.pdf).
The graphs are stored line-by-line in graph6 format for compact storage and easy reading. More about the format can be found here: https://users.cecs.anu.edu.au/~bdm/data/formats.html
The first number in the file name indicates k and the last indicates the order of the graph.
The sage code used to generate the graphs is available in the Jupyter notebook file (k-vertex-critical_P5gem-free_generator.ipynb) for easy viewing.