There are several theorems that will tell you when a graph is Hamiltonian.Dirac’s theorem:...

There are several theorems that will tell you when a graph is Hamiltonian.

Dirac’s theorem:If a simple* graph has n vertices where n ≥ 3 and each vertex has at least  edges joined to it, then the graph is Hamiltonian. *Simple means that any two vertices in the graph have at most one edge between them and no vertex has an edge to itself.

Ore’s theorem:If a graph has n vertices where n ≥ 2 and for any two nonadjacent vertices the sum of their degrees is at least n, then the graph is Hamiltonian.

Determine: a) Are the conditions of Dirac’s theorem satisfied? b) Are the conditions of Ore’s theorem satisfied? c) Is the graph Hamiltonian?