29.1.7. Question 6

Try these first

1. 1.

   What is the complement of a graph?

   Hint

   Consider what edges exist in the original graph.

2. 2.

   If H is a subgraph of G, what is one potential outcome for H'?

   Hint

   Think of how edges relate in complements.

3. 3.

   If H is a subgraph of G, what can we say about H' regarding G'?

   • H' is always a subgraph of G'
   • H' may not be a subgraph of G'
   • H' is identical to G'

   Hint

   Think of how edges in complements might change.

4. 4.

   True or False: A graph and its complement must always share the same number of vertices.

   • True
   • False

   Hint

   Consider the definition of a complement.

5. 5.

   Devise a connected graph G and its subgraph H such that the complement of the subgraph H' avoids being a true subgraph of G's complement G'.

   Hint

   Visualize the square and track each edge's existence.

6. 6.

   Using a given graph, manually determine and plot its complement, exploring vertex relationships therein.

   Hint

   Connect each node and observe missing edges.