1.2. Subgraph of a Graph

Try these first

1. 1.

   Define what a subgraph is.

   Hint

   Think about which parts of a graph are used to create a subgraph.

2. 2.

   What differentiates a proper subgraph from a regular subgraph?

   Hint

   It must have fewer elements than the parent graph.

3. 3.

   What is a subgraph?

   • A complete graph
   • All vertices of G
   • A graph formed from a subset of vertices and edges of G

   Hint

   Focus on how subgraphs are formed.

4. 4.

   True or False: An induced subgraph can contain edges connecting vertices not in the subset.

   • True
   • False

   Hint

   Think carefully about the definition of induced subgraphs.

5. 5.

   Given a graph G with vertices A, B, C, D, and edges covering all pairs of these vertices, create a proper subgraph and identify whether it remains connected.

   Hint

   Determine adjacent vertices to include an edge.

6. 6.

   Explain in detail the significance of induced subgraphs and how they apply in real-life scenarios, such as social networks or transportation systems.

   Hint

   Consider how focusing on groups simplifies complex relationships.