Special Graphs

4. A subgraph of a graph $G$ is a graph formed using a subset of the vertices and a subset of the edges of $G$.
   
   Meaning, to generate a subgraph of $G$, you would delete at least one of $G$'s edges or vertices.
   

   Removing the node $4$, the edges connected to it, and one more edge $\{2, 3\}$, create a subgraph (right) of $G$. Miriam Briskman, CC BY-NC 4.0.

   \documentclass[border=1pt]{standalone}
   \usepackage{tikz}
   
   \tikzset{
   vertex/.style={draw, circle, very thick, minimum size=1cm},
   edge/.style={very thick}
   }
   
   \begin{document}
   
   \begin{tikzpicture}
   
   \node[vertex] (1) at (0,0) {$1$};
   \node[vertex] (2) at (3,0) {$2$};
   \node[vertex] (3) at (1.5,2) {$3$};
   \node[vertex] (4) at (1.5,-2) {$4$};
   
   \draw[edge] (1) -- (2);
   \draw[edge] (2) -- (3);
   \draw[edge] (3) -- (1);
   \draw[edge] (1) -- (4);
   \draw[edge] (2) -- (4);
   
   \draw (4.5,2.5) -- (4.5,-2.5);
   
   \node[vertex] (5) at (6,0) {$1$};
   \node[vertex] (6) at (9,0) {$2$};
   \node[vertex] (7) at (7.5,2) {$3$};
   
   \draw[edge] (5) -- (6);
   \draw[edge] (7) -- (5);
   
   \end{tikzpicture}
   
   \end{document}