1.3. Proper Subgraph

Try these first

1. 1.

   Define what a proper subgraph is.

   Hint

   Think about what makes a subset distinct.

2. 2.

   What is an induced subgraph?

   Hint

   Consider the vertex connections.

3. 3.

   What defines a proper subgraph?

   • Contains all vertices and edges
   • Is different from the parent graph
   • Has no relation to the parent graph

   Hint

   Focus on the relationship to the parent graph.

4. 4.

   A proper subgraph can include which of the following?

   • True
   • False

   Hint

   Think about subset relationships.

5. 5.

   Given graph G with vertices {A, B, C, D} and edges {(A, B), (B, C), (C, D)}, identify a proper subgraph and explain how it is determined.

   Hint

   Look for missing connections.

6. 6.

   Create a graph with an induced subgraph that is also a proper subgraph. Explain your reasoning.

   Hint

   Consider vertex connections carefully.