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petersen graph
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Undergraduate
By
Shiva Kintali
on Oct. 3, 2013 | Updated Jan. 4, 2018
Planar graphs and girth
Let \(G\) be an \(n\)-vertex simple connected planar graph with girth \(k\). Prove that \(G\) has at most \((n-2)\cdot \frac{k}{k-2}\) edges. Use this to prove that the Petersen graph is nonplan…
Mathematics
Graph Theory
eulers formula
girth
petersen graph
planar graphs
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Undergraduate
By
Shiva Kintali
on June 5, 2012 | Updated Dec. 6, 2017
Properties of Petersen Graph
Petersen Graph is the graph shown below : Prove the following properties of the Petersen Graph : It is not planar. It is strongly-regular. It has a Hamiltonian path but no Hamiltonian Cycle. It i…
Mathematics
Graph Theory
connectivity
hamiltonian cycle
matching
petersen graph
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Undergraduate
By
Shiva Kintali
on June 8, 2013 | Updated Dec. 6, 2017
Petersen graph has ten 6-cycles
Petersen Graph is the graph shown below : Prove the following : If two vertices are non-adjacent in the Petersen Graph, then they have exactly one common neighbor. Petersen graph is 3-regular, so…
Mathematics
Graph Theory
counting
petersen graph
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