        \problemdata       % Takes 5 *mandatory* arguments
        {adj-mat}             % latex-friendly label for the prob.
        {graphs}  % The topic(s) of the problem content.
        {}               % Source (if known)
        {F01 PS4-2} % Usage (list ones you are aware of).
        {}        % Last revision info (author, date).


\begin{problem}
The adjacency matrix of a graph is given below.

\[
\left[
\begin{array}{cccccc}
0 & 1 & 1 & 1 & 0 & 1 \\
1 & 0 & 0 & 1 & 1 & 1 \\
1 & 0 & 0 & 1 & 1 & 1 \\
1 & 1 & 1 & 0 & 1 & 0 \\
0 & 1 & 1 & 1 & 0 & 1 \\
1 & 1 & 1 & 0 & 1 & 0
\end{array}
\right]
\]

\begin{problemparts}

\problempart Draw the graph defined by this adjacency matrix.  Label
the vertices of your graph $1, 2, \ldots, 6$ so that vertex $i$
corresponds to row and column $i$ of the matrix.

\solution{ 
\begin{center}
\includegraphics[width=2in,height=2in]{figures/adjgraph}
\end{center}
%%\centerline{\resizebox{!}{2.0in}{\includegraphics{figures/adjgraph}}}
}

\problempart Give a coloring of the vertices that uses the minimum
number of colors. Prove that this a minimum coloring.

\solution{The diagram above shows a 3-coloring.  The chromatic number
cannot be less than 3, because vertices 1, 2, and 4 are all connected
and therefore must receive distinct colors.  Consequently, the
chromatic number of the graph is exactly 3.}

\end{problemparts}

\end{problem}