5.1. Discrete Mathematics

Try these first

1. 1.

   What is a degree sequence?

   Hint

   Think about how we organize the degrees.

2. 2.

   Can a degree sequence have negative values?

   Hint

   Consider what a negative degree would imply.

3. 3.

   Is the degree sequence (4, 3, 3, 2) graphic?

   • True
   • False

   Hint

   Try imagining the graph layout.

4. 4.

   What must the sum of degrees be equal to in a simple graph?

   • Odd number
   • Even number
   • None of the above

   Hint

   Consider how many edges connect vertices.

5. 5.

   Given the degree sequence (7, 3, 2, 2, 1), can you construct a valid simple graph? Explain your steps.

   Hint

   Check progression after each reduction.

6. 6.

   If the degree sequence is (3, 3, 3, 3, 3), how many edges does the graph have? Illustrate it.

   Hint

   Use the sum of degrees formula.