4.3. Question 2

Try these first

1. 1.

   What does deleting a vertex from a graph do?

   Hint

   Think of how a tree branch would behave if you cut it.

2. 2.

   If a graph has a degree of 3 for vertex v1, how many edges are removed if v1 is deleted?

   Hint

   The degree indicates the number of connections.

3. 3.

   What happens to the total number of edges when a vertex is deleted?

   • It stays the same
   • It decreases by the degree of the vertex
   • It increases by the degree of the vertex

   Hint

   Remember the rule of vertex deletion.

4. 4.

   True or False: The handshaking theorem states that the sum of degrees divided by two equals the cardinality of edges.

   • True
   • False

   Hint

   Recall the fundamental principles of edge connections.

5. 5.

   Suppose a graph has a total of 10 vertices. If removing each vertex results in 9, 8, 7, 6, 5, 4 edges respectively, predict the total edge count.

   Hint

   Count how many edges were lost and anticipate the starting number.

6. 6.

   Given a graph of 5 vertices where three vertices have degrees of 2, 2, and 1 when others are removed, calculate its full edge set.

   Hint

   Count up and think logically, relate back to handshaking principles.