18.2.1. Abstract Representation of the Problem

Try these first

1. 1.

   What is a vertex in graph theory?

   Hint

   It's one of the main components of a graph.

2. 2.

   Define an edge.

   Hint

   Think of it as a line connecting two points.

3. 3.

   What is the primary component of a graph?

   • Vertices
   • Edges
   • Both

   Hint

   Think about the two main features of any graph.

4. 4.

   True or False: The Four Color Theorem applies to three-dimensional graphs.

   • True
   • False

   Hint

   Consider the dimensionality of the graphs described.

5. 5.

   Given a graph with numerous interconnected cities, design a coloring scheme that minimizes colors while ensuring no two adjacent cities are the same color. Explain your reasoning.

   Hint

   Visualize the graph and strategize.

6. 6.

   In a school, each class can be represented as a vertex and subject overlaps as edges. If one class is assigned a color that another class can't share, how can you organize them efficiently?

   Hint

   Create a visual representation to help with this problem.