A country has five states, \(A, B, C, D\) and \(E\).

A graph can be drawn with vertices to represent each of the states.

Edges represent a border shared between two states.

- What is the sum of the degrees of the vertices of the graph above? (1 mark)

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- Euler's formula, \(v+f=e+2\), holds for this graph.

- Complete the formula by writing the appropriate numbers in the boxes provided below. (1 mark)

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- Complete the sentence by writing the appropriate word in the space provided below. (1 mark)

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- Euler’s formula holds for this graph because the graph is connected and ______________.

- Complete the formula by writing the appropriate numbers in the boxes provided below. (1 mark)
- The diagram below shows the position of state \(A\) on a map of this country.
- The four other states are indicated on the diagram as 1, 2, 3 and 4.

- Use the information in the graph above to complete the table below. Match the state \((B, C, D\) and \(E)\) with the corresponding state number \((1,2,3\) and 4\()\) given in the map above. (1 mark)

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\begin{array} {|c|c|}

\hline

\rule{0pt}{2.5ex} \quad \quad \textbf{State} \quad \quad \rule[-1ex]{0pt}{0pt} & \textbf{State Number} \\

\hline

\rule{0pt}{2.5ex} B \rule[-1ex]{0pt}{0pt} &\\

\hline

\rule{0pt}{2.5ex} C \rule[-1ex]{0pt}{0pt} & \\

\hline

\rule{0pt}{2.5ex} D \rule[-1ex]{0pt}{0pt} & \\

\hline

\rule{0pt}{2.5ex} E \rule[-1ex]{0pt}{0pt} & \\

\hline

\end{array}