24.1.3. Simple Graph Definition

Try these first

1. 1.

   What is a graph?

   Hint

   Think about how you can visualize connections.

2. 2.

   What does it mean for a graph to be directed?

   Hint

   Consider a one-way street for directions.

3. 3.

   What is the defining characteristic of a simple graph?

   • A graph with many edges between nodes.
   • A graph with no self-loops and at most one edge between any two vertices.
   • A graph with no edges.

   Hint

   Think about the restrictions placed on connections.

4. 4.

   True or False: In a directed graph, edges can be traversed in both directions.

   • True
   • False

   Hint

   Consider how directed edges behave.

5. 5.

   Create a simple graph with at least 4 vertices and demonstrate the degrees of each vertex. Explain any observations you make.

   Hint

   Ensure your graph clearly shows connections and follows the simple graph criteria.

6. 6.

   Discuss how adding a self-loop to a vertex changes the properties of a simple graph. Give an example.

   Hint

   Recall how degrees are calculated and what constitutes a simple graph.