% Chris Hanusa
% chanusa@qc.cuny.edu	
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\begin{center}\large 
MATH 634, Spring 2014

{\sc Homework 10}

due 5:00{\sc pm} on Monday, March 10.
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\smallskip\noindent
{\color{red} Follow the posted homework guidelines when completing this assignment.}

\smallskip\noindent
Problems {\bf 10E},  {\bf 10G}, and  {\bf 10P} should be typed (or written up) and handed in as class starts on Monday 3/10:

\begin{enumerate}
\item[\bf 10E.]  
Determine the vertex connectivity, edge connectivity, clique number, and independence number of each of the graphs below. (You can ignore the loop in Graph $G_4$ if it bothers you.)

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\includegraphics[height=4in]{connectivity.eps}
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\item[\bf 10G.] 
Determine the girth and the diameter of the following graphs: $K_n$, $K_{m,n}$, Petersen, Dodecahedron, 5D-cube. 

Justify your answers and make sure to account for initial cases if they are different.

\item[\bf 10P.]  
\begin{enumerate}
\item Prove or disprove: Every 3-connected graph has no bridge. 
\item Prove or disprove: Every 3-edge-connected graph has no cut vertex.
\item In a graph with vertex connectivity at least two, find an example of a minimal cut set that is not a minimum cut set.
\end{enumerate}


\end{enumerate}



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