12. Graph Theory

Using the graph below, determine if the sequence of vertices describes a Hamilton path (H.P.), a Hamilton circuit (H.C.), or neither.

$Q,U,P,Q,T,S,R$

Using the graph below, determine if the sequence of vertices describes a Hamilton path (H.P.), a Hamilton circuit (H.C.), or neither.

$P,Q,T,S,R,U,P$

Using the graph below, determine if the sequence of vertices describes a Hamilton path (H.P.), a Hamilton circuit (H.C.), or neither.

$Q,P,U,R,S,T$

Determine if the graph must have Hamilton circuits. If so, how many?

Note: We will be using the formula below.

Complete? ☐

# of vertices: ___

# of Hamilton circuits: ___