\documentclass[11pt]{report}
\input{header}
\pagestyle{empty}
\begin{document}
\begin{tabular}{ccc}
  \begin{tikzpicture}
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    \node[point] at (5,6) (b) {};
    \node[point] at (9,4) (c) {};
    \node[point] at (7,2) (d) {};
    \node[point] at (3,1) (e) {};
    \node[point] at (3,2) (f) {};
    \draw[blue,very thick](a)--(b);
    \draw[blue,very thick](b)--(c);
    \draw[blue,very thick](c)--(d);
    \draw[blue,very thick](d)--(e);
    \draw[blue,very thick](e)--(f);
    \draw[blue,very thick](f)--(a);
    \node[point=cyan,label={[label distance=0pt]135:{$v_1$}}] at (3,3) (1) {};
    \node[point=cyan,label={[label distance=0pt]135:{$v_2$}}] at (6,4) (2) {};
    \draw[dashed,blue,very thick] (1)--(2);
    \draw[halfedge] (1) to (2);
    \draw[halfedge] (2) to (1);
    \node at (5,5) {$f$};
    \draw[thin](0.5,0) rectangle (10,7);
  \end{tikzpicture} &
  %
  \begin{tikzpicture}
    \node[point] at (1,3) (a) {};
    \node[point] at (2,5) (b) {};
    \node[point] at (5,6) (c) {};
    \node[point,label={[label distance=0pt]180:{$u$}}] at (7,3) (u) {};
    \node[point] at (5,1) (e) {};
    \node[point] at (3,2) (f) {};
    \node[point] at (2,1) (g) {};
    \draw[blue,very thick](a)--(b);
    \draw[blue,very thick](b)--(c);
    \draw[blue,very thick](c)--(u);
    \draw[blue,very thick](u)--(e);
    \draw[blue,very thick](e)--(f);
    \draw[blue,very thick](f)--(g);
    \draw[blue,very thick](g)--(a);
    \node[point=cyan,label={[label distance=0pt]90:{$v$}}] at (9,4) (v) {};
    \draw[dashed,blue,very thick] (u)--(v);
    \draw[dashed,halfedge] (c) to (u);
    \draw[dashed,halfedge] (u) to (e);
    \draw[halfedge] (u) to (v);
    \draw[halfedge] (v) to (u);
    \draw[thin] (0.5,0) rectangle (10,7);
  \end{tikzpicture} &
  %
  \begin{tikzpicture}
    \node[point] at (1,3) (a) {};
    \node[point] at (2,6) (b) {};
    \node[point,label={[label distance=0pt]45:{$u_1$}}] at (5,6) (1) {};
    \node[point,label={[label distance=0pt]45:{$u_2$}}] at (7,1) (2) {};
    \node[point] at (4,2) (e) {};
    \node[point] at (2,1) (f) {};
    \draw[blue,very thick](a)--(b);
    \draw[blue,very thick](b)--(1);
    \draw[dashed,thick,halfedge] (b) to (1);
    \draw[dashed,thick,halfedge] (1) to (b);
    \draw[dashed,blue,very thick](1)--(2);
    \draw[thick,halfedge] (1) to (2);
    \draw[thick,halfedge,shorten <=4pt] (2) to (1);
    \draw[blue,very thick] (2)--(e);
    \draw[dashed,halfedge] (2) to (e);
    \draw[dashed,halfedge,shorten >=4pt] (e) to (2);
    \draw[blue,very thick] (e)--(f);
    \draw[blue,very thick] (f)--(a);
    \node[point] at (2.5,4) (a) {};
    \node[point] at (3.5,5) (b) {};
    \node[point] at (4.5,4) (c) {};
    \node[point] at (3.5,3) (d) {};
    \draw[blue,very thick](a)--(b);
    \draw[blue,very thick](b)--(c);
    \draw[blue,very thick](c)-- node[midway,below,sloped] {$h_1$} (d);
    \draw[blue,very thick](d)--(a);
    \draw[blue,very thick](a)--(c);
    \node at (1,5) {$f$};
    \node at (2.5,5) {$f'$};
    \node[point] at (7,4) (a) {};
    \node[point] at (8,4) (b) {};
    \node[point] at (8,5) (c) {};
    \node[point] at (9,3) (d) {};
    \draw[blue,very thick] (a)--(b);
    \draw[blue,very thick] (b)--(c);
    \draw[blue,very thick] (c)--(a);
    \draw[blue,very thick] (b)-- node[midway,below,sloped] {$h_2$} (d);
    \draw[thin] (0.5,0) rectangle (10,7);
  \end{tikzpicture}
\end{tabular}
\end{document}
