Minor Minimal Non-Apex Graphs

The first link is a file with all the MMNA graphs of order up to and including 12, and all the MMNA graphs of size up to and including 26. The second file contains MMNA graphs not in the first list.

All 295 MMNA graphs of order up to 12 and size up to 26.

Extra 44 MMNA graphs of larger order and size.

Maximal Linklessly Embeddable Graphs

These lists were computed using the nauty program of Brendan McKay, the Mathematica program written by Ramin Naimi, and a Python script written by Ryan Odeneal. The lists are complete up to and including order 12, the rest are just samples.

References

For graphs of order up to 11.

Odeneal, R., Naimi, R., Pavelescu, A., & Pavelescu, E. (2022). The complement problem for linklessly embeddable graphs. Journal of Knot Theory and Its Ramifications, 31(11), 2250075.

For graphs of order 12.

Li, G., Pavelescu, A., & Pavelescu, E. (2026). Intrinsically knotted graphs and connected domination. AUSTRALASIAN JOURNAL OF COMBINATORICS, 94(1), 25-49.