The Petersen graph is an undirected graph of with 10 vertices and 15 edges. In graph theory, it provides many counterexamples. The Petersen graph has many interesting properties:1
- It’s nonplanar
- It has chromatic number 3
- It has crossing number 2
- It has orientable genus 1
- It has non-orientable genus 1
- It is a unit distance graph
- It is strongly regular
- It is symmetric
- It is one of only 13 cubic distance-regular graphs
- It has a Hamiltonian path but no Hamiltonian cycle
- It is the smallest vertex-transitive graph that is not a Cayley graph
- It has chromatic index 4
The list goes on….
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References
- Petersen Graph http://en.wikipedia.org/wiki/Petersen_graph Accessed 25/09/09.
