1.4. Induced Subgraph

Try these first

1. 1.

   Define an induced subgraph.

   Hint

   Think about the subset of vertices and how edges are treated.

2. 2.

   What is the difference between a subgraph and a proper subgraph?

   Hint

   Focus on the criteria that separates these types.

3. 3.

   What defines an induced subgraph?

   • A subgraph with all edges intact
   • A subgraph only containing selected vertices and their connecting edges
   • A subgraph with no edges

   Hint

   Focus on what makes the edges part of the induced subgraph.

4. 4.

   True or False: An induced subgraph can have edges that connect vertices not in the selected set.

   • True
   • False

   Hint

   Reflect on the definition of how induced subgraphs function.

5. 5.

   Consider a graph consisting of vertices {a, b, c, d, e} and edges {(a, b), (b, c), (a, c), (c, d)}. If we select W = {a, b, d}, describe the edges in the induced subgraph.

   Hint

   Study the connections based on the selected vertices carefully.

6. 6.

   In a real-world scenario, explain how you might use induced subgraphs to study a social network and provide an example with 3 vertices.

   Hint

   Consider the network structure and relationship implications.