Practice Question 6 (29.1.7) - Introduction to Tutorial 8 - Discrete Mathematics

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6 sample questions

Question 1.
What is the complement of a graph?
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Consider what edges exist in the original graph.
Question 2.
If H is a subgraph of G, what is one potential outcome for H'?
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Think of how edges relate in complements.
3Question 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'
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Think of how edges in complements might change.
4Question 4.
True or False: A graph and its complement must always share the same number of vertices.
- True
- False
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Consider the definition of a complement.
Question 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'.
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Visualize the square and track each edge's existence.
Question 6.
Using a given graph, manually determine and plot its complement, exploring vertex relationships therein.
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Connect each node and observe missing edges.

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