12.5. Independent Set Problem

Try these first

1. 1.

   Define what an independent set is.

   Hint

   Think about the connections between vertices.

2. 2.

   Can a single vertex form an independent set?

   Hint

   Consider whether it has edges connecting to anything else.

3. 3.

   What defines an independent set?

   • Connected vertices
   • Unconnected vertices
   • Vertices with edges

   Hint

   Think about how edges relate to vertices.

4. 4.

   True or False: An independent set can contain two directly connected vertices.

   • True
   • False

   Hint

   Recall what makes a set independent.

5. 5.

   Given a complex graph with vertices numbered from 1 to 10 and edges connecting every vertex to two others, determine the largest possible independent set and justify your reasoning.

   Hint

   Consider connections carefully before making selections.

6. 6.

   Construct a graph and demonstrate two different independent sets within it. Highlight the differences in edge connections.

   Hint

   Map edges clearly to visualize independence.