\documentclass[12pt]{article}
\usepackage{latexsym}
\usepackage{amssymb,amsmath}
\usepackage[pdftex]{graphicx}
\usepackage{hyperref}
\topmargin = 0.1in \textwidth=5.7in \textheight=8.6in
\oddsidemargin = 0.2in \evensidemargin = 0.2in
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
\begin{document}
\begin{center}
\large
COMPUTER SCIENCE 20, SPRING 2012 \\
DISCRETE MATHEMATICS FOR COMPUTER SCIENCE\\
\medskip
Class \#16 (Directed Graphs)
\end{center}
\paragraph{Homework, due in hard copy Wednesday 3/7/2012 at 10:10am}
\paragraph{Please write your TF's name on your homework, and list the names of any students with whom you collaborated.}
\begin{enumerate}
\item A directed tree is a special type of directed graph that has the following two properties:
\begin{itemize}
\item all vertices in a directed tree have in-degree at most one.
\item any pair of two distinct vertices in a tree is connected by \emph{exactly} one path (in other words, for every pair of vertices $A$ and $B$, $A\rightarrow B$ XOR $B\rightarrow A$).\end{itemize}
\begin{enumerate}
\item Prove that if a graph $G$ is a directed tree, then $G$ is a DAG.
\item Prove that if a graph $G$ is a directed tree, then it has exactly one vertex with in-degree zero.
\item Prove that all directed trees with $n$ vertices have exactly $n-1$ edges.
\end{enumerate}
\end{enumerate}
\end{document}