CS$357-$ Cyclone Lab Sheet A

Try to use the online editor to finish the lab. The online editor is here.

IMPORTANT: Make sure you get marked before leaving the lab and don't forget to submit your $.$cyclone file on moodle before Friday $(23$:$59,13$th$-$December$)$

$-$ Petersen Graph

A petersen graph is an interesting undirected graph. It has $10$ vertices $($nodes$)$ and $15$ edges$($See the following picture$).$ This graph is a small graph that is used to show many useful examples and counterexamples in graph theory.

One of the many its interesting properties is to do with Hamiltonian path$/$cycle$.$ In this lab, your main goal is to prove that a petersen graph is not Hamiltonian. What does it mean? It means that a petersen graph contains no Hamiltonian cycle.

Use Cyclone to show that

$-$ A petersen graph has no Hamiltonian cycle.

$-$ A petersen graph has at least one Hamiltonian path.

A Hamiltonian path is a path that visits each vertex $($node$)$ exactly once. A Hamiltonian cycle is a cycle that visits each vertex $($node$)$ exactly once $($except for the starting vertex$/$node$).$