The weights on the graph below represent distances (in miles). Find the total distance (weight) of each path or circuit.

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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: ___

How many Hamilton circuits exist in a complete graph with the given number of vertices, $n$?

Note: We will be using the formula below.

$n=3$

How many Hamilton circuits exist in a complete graph with the given number of vertices, $n$ ?

Note: We will be using the formula below.

$n=12$

The weights on the graph below represent distances (in miles). Find the total distance (weight) of each path or circuit.

Home, Grocery Store, Post Office, Bank