Here, the - transform corresponds to replacing the
three graph edges forming a triangle
graph
are by three graph edges and a new graph
vertex that form a , and the - transform to the reverse operation of this.

Sachs (1983) showed that the seven graphs of the Petersen family are intrinsically linked, i.e., no matter how they are embedded in space, they have cycles that
are linked to each other. He also suggested characterization of these graphs via
forbidden subgraphs. Robertson et al. (1993)
resolved this question by establishing that intrinsically
linked graphs are characterized by having a member of the Petersen family as
a graph minor.

In addition, the Petersen family graphs are among the forbidden minorsForbidden Minor
of apex graphs.

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.
New York: W. H. Freeman, pp. 221-222, 1994.Robertson, N.;
Seymour, P. D.; and Thomas, R. "'Linkless Embeddings of Graphs in 3-Space."
Bull. Amer. Math. Soc.28, 84-89, 1993.Sachs, H. "On
a Spatial Analogue of Kuratowski's Theorem on Planar Graphs--An Open Problem".
In Graph Theory: Proceedings of a Conference held in Łagòw, Poland,
February 10Ð13, 1981 (Ed. M. Horowiecki, J. W. Kennedy, and
M. M. Sysło). New York: Springer-Verlag, pp. 230-241, 1983.