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\begin{document}
\title{Math 101 Homework}
\author{Mary Radcliffe}
\date{due 15 Jan 2015}
\maketitle

Complete the following problems. Fully justify each response.

\begin{enumerate}

\item Suppose you have a graph with 5 vertices. What is the maximum number of edges it can have? 

\item Suppose you have a graph with $n$ vertices. What is the maximum number of edges it can have? Explain your answer.

\item Show that the two graphs in the figure below are isomorphic by finding an isomorphism between them.
\begin{figure}[htp]
\centering
\includegraphics[width=.8\textwidth]{pic.pdf}
\end{figure}

\item Spend at least 5-10 minutes playing \href{http://planarity.net/}{Planarity}. While you're playing, remember that every time you move vertices around, you are always looking at the \textit{same} graph, but a \textit{different} embedding.

\end{enumerate}

\end{document}