29.2. Graph Theory Concepts

Try these first

1. 1.

   What is the complement of a complete graph with 3 vertices?

   Hint

   Consider what edges would exist.

2. 2.

   Define a tree in your own words.

   Hint

   Think about connections and loops.

3. 3.

   What is the definition of a graph?

   • A collection of vertices and edges
   • A matrix of numbers
   • A type of equation

   Hint

   Think about how graphs represent relationships.

4. 4.

   True or False: The complement of graph G contains all edges from G.

   • True
   • False

   Hint

   Remember the definition of a complement.

5. 5.

   Construct a graph with 10 vertices that is self-complementary and verify its properties.

   Hint

   Utilize the 4k + 1 framework.

6. 6.

   Demonstrate, through example, how the removal of an edge in a tree splits it into two components.

   Hint

   Remember that trees are connected, and removing edges has specific consequences.