Special Graphs

5. An induced subgraph is formed from a subset of vertices together with all edges connecting those vertices in the original graph.
   

   Removing vertex 4 and only the edges that were connected to this vertex 4 (but no other edges) creates an induced subgraph 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] (6) -- (7);
   \draw[edge] (7) -- (5);
   
   \end{tikzpicture}
   
   \end{document}