1.5. Set Theoretic Operations on Graphs

Try these first

1. 1.

   Define a subgraph.

   Hint

   Think about how a subgraph relates to a larger graph.

2. 2.

   What distinguishes a proper subgraph from a general subgraph?

   Hint

   Comparison helps here: think of identical vs non-identical.

3. 3.

   What is a proper subgraph?

   • A subgraph that includes all edges and vertices of the original graph
   • A subgraph that is not identical to the original graph
   • A graph with fewer vertices than edges

   Hint

   It's about comparison; think non-identity.

4. 4.

   True or False: Removing an edge from a graph also removes the connected vertices.

   • True
   • False

   Hint

   Consider the independence of edges versus vertices.

5. 5.

   Given a graph with vertices A, B, C, and edges AB, AC, BC. If edges AB and AC are removed, describe the resulting graph with vertex C remaining.

   Hint

   Focus on the connections surrounding the vertex in question.

6. 6.

   Create an example of a proper subgraph from a larger graph while ensuring none of its vertices or edges match the original graph.

   Hint

   Think of combining elements without overlapping fully.