Related Graphs
The generalized Petersen graph G(n,k) is formed by connecting the vertices of a regular n-gon to the corresponding vertices of a star polygon with Schläfli symbol {n/k}. For instance, in this notation, the Petersen graph is G(5,2): it can be formed by connecting corresponding vertices of a pentagon and five-point star, and the edges in the star connect every second vertex. The generalized Petersen graphs also include the n-prism G(n,1) the Dürer graph G(6,2), the Möbius-Kantor graph G(8,3), the dodecahedron G(10,2), the Desargues graph G(10,3) and the Nauru graph G(12,5).
The Petersen family consists of the seven graphs that can be formed from the Petersen graph by zero or more applications of Δ-Y or Y-Δ transforms. The complete graph K6 is also in the Petersen family. These graphs form the forbidden minors for linklessly embeddable graphs, graphs that can be embedded into three-dimensional space in such a way that no two cycles in the graph are linked.
The Clebsch graph contains many copies of the Petersen graph as induced subgraphs: for each vertex v of the Clebsch graph, the ten non-neighbors of v induce a copy of the Petersen graph.
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