[Tex/LaTex] Help in drawing a graph (graph theory)

graphicstikz-pgf

Can anyone help me to write the code to have the same graph as in the image below?

enter image description here

\begin{tikzpicture}
    \matrix[column sep=2em, row sep=10ex, inner sep=0pt, minimum width=6pt] (M) {%
        \node[mypoint, label={[left,xshift=-4pt]V1}, fill=green] (V1) {}; & & & & & \node[mypoint, label={above:$V_{2}$}] (V2) {};\\


        \node[mypoint, label={[left,xshift=-4pt]V5}] (V5) {}; & & & & &  
        \node[mypoint, label={below left:V4}] (V4) {}; & & & & &  
        \node[mypoint, label={[right,xshift=2pt]V3}] (V3) {};\\
    };
    \draw (V1) -- (V2);
    \draw (V5) -- (V1);
    \draw (V5) -- (V4);

\end{tikzpicture}

Best Answer

enter image description here

\documentclass[12pt]{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (-2.,0.)-- (2.,0.);
\draw(-2.,-1.) circle (1.cm);
\draw (-2.,4.)-- (-2.,0.);
\draw [rotate around={0.:(0.,4.)}] (0.,4.) ellipse (2.1cm and 0.5cm);
\draw (0.2,5.2) node[anchor=north west] {$e_1$};
\draw (0.2,3.4) node[anchor=north west] {$e_2$};
\draw (2.1,4.3) node[anchor=north west] {$v_4$};
\draw (-2.7,4.4) node[anchor=north west] {$v_3$};
\draw (-2.7,2.3) node[anchor=north west] {$e_3$};
\draw (2.2,0.4) node[anchor=north west] {$v_1$};
\draw (-2.8,0.4) node[anchor=north west] {$v_2$};
\draw (-2.8,-2.0) node[anchor=north west] {$e_4$};
\draw (0.1,-0.1) node[anchor=north west] {$e_5$};
\begin{scriptsize}
\draw [fill=black] (-2.,0.) circle (3.5pt);
\draw [fill=black] (2.,0.) circle (3.5pt);
\draw [fill=black] (-2.,4.) circle (3.5pt);
\draw [fill=black] (2.,4.) circle (3.5pt);
\end{scriptsize}
\end{tikzpicture}
\end{document}