24.1.1. Definition of a Graph

Try these first

1. 1.

   What are the two main components of a graph?

   Hint

   Think of what makes up a graph.

2. 2.

   Define a directed graph.

   Hint

   Does direction matter in this type of graph?

3. 3.

   What is a graph?

   • A collection of points
   • A collection of vertices and edges
   • A type of equation

   Hint

   Consider what components make up the structure of a graph.

4. 4.

   In a directed graph, do edges show direction?

   • True
   • False

   Hint

   Think about the meaning of directed edges.

5. 5.

   Given a graph with 4 vertices and edges between vertices 1-2, 2-3, 3-4, and 4-1, calculate the degree of each vertex and verify the handshaking theorem.

   Hint

   Count the connections starting from every vertex.

6. 6.

   Construct a directed graph with at least three vertices where one vertex has a self-loop. Describe its edge and vertex characteristics.

   Hint

   Remember how self-loops affect the degree count.