\documentclass{article}
\usepackage{tikz}
\usepackage{xepersian}
\begin{document}

$$V=\{a, b, c, d, e, f, g\}$$
$$V_{1}=\{a, b, c, d\}$$
$$E=\{\{a, b\}, \{a, c\}, \{b, c\}, \{c,d\}, \{a, e\}, \{a, f\}, \{d, e\}, \{c, f\}, \{d, g\}\}$$
\begin{center}
\begin{tikzpicture}
 \caption{ $\phi(V_{1}, V-V_{1}, E)$}
 \label{fig1.1}
\filldraw [black]
 (0,0) circle (2pt)
(1,0) circle (2pt)
(2,0) circle (2pt)
(2,1) circle (2pt)
(1.65,1.65) circle (2pt)
(1,2) circle (2pt)
(0.25,1.5) circle (2pt);
\draw (0.25,1.5)-- (1,2);
\draw (1.65,1.65)-- (1,2);
\draw (1.65,1.65)-- (2,1);
\draw (2,0)-- (2,1);
\draw (1.65,1.65)-- (0.25,1.5);
\draw (1.65,1.65)-- (1,0);
\draw (0.25,1.5)-- (1,0);
\draw (0.25,1.5)-- (0,0);
\draw (2,1)-- (0,0);
\node[left] at (0,0) {$e$};
\node[below] at (1,0) {$f$};
\node[left] at(2,0){$g$};
\node[right] at(2,1) {$d$};
\node[right] at(1.65,1.65) {$c$};
\node[above] at(1,2) {$b$};
\node[left] at(0.25,1.5) {$a$};

\end{tikzpicture}
\end{center}
\end{document}