Lesson DA4-DA5
DA4-DA5 Planarity, complete and bipartite graphs Quiz: AQA Further Maths, Unit 5
20 questions
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Lesson DA4-DA5, Planarity, complete and bipartite graphs: 20 multiple choice questions for the AQA Further Maths (7367), Unit 5: Optional application 3: discrete mathematics, written with Revision Ninja.
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The 20 questions
-
According to Kuratowski's theorem, a graph is non-planar if it contains a subdivision of which graphs?
- K4 or K2,3
- K3 or K2,2
- K6 or K4,4
- K5 or K3,3
-
In a complete graph Kn, how many edges connect each pair of distinct vertices?
- Exactly one
- Exactly two
- At least one
- Zero
-
In a bipartite graph, between which sets of vertices can edges exist?
- Any arbitrary sets
- The same set
- Two disjoint sets
- Three disjoint sets
-
Which edges are included in the complement of a simple graph G?
- Edges forming cycles
- All possible edges
- Connected vertex pairs
- Unconnected vertex pairs
-
How many edges does the complete graph K7 have?
- 49
- 21
- 42
- 14
-
How many edges does the complete bipartite graph K3,4 have?
- 6
- 12
- 7
- 24
-
The complete bipartite graph K3,3 has 6 vertices. How many edges does its complement have?
- 3
- 12
- 9
- 6
-
What is the maximum number of edges a simple planar graph with 6 vertices can have?
- 9
- 10
- 12
- 15
-
What is the maximum number of edges a simple bipartite planar graph with 6 vertices can have?
- 6
- 9
- 8
- 12
-
Which of the following graphs is non-planar according to Kuratowski's theorem?
- K2,4
- K3,3
- K4
- K2,3
-
A simple graph has 5 edges. What is the sum of all the entries in its adjacency matrix?
- 25
- 20
- 5
- 10
-
In an adjacency matrix of a simple graph, what does a row sum represent?
- Chromatic number
- Number of paths
- Total edge count
- Vertex degree
-
Can a graph containing a cycle of odd length be bipartite?
- Never
- Only if connected
- Always
- Only if complete
-
What maximum number of edges can a simple planar graph with 5 vertices have?
- 10
- 9
- 12
- 8
-
What is the planarity status of the complete bipartite graph K2,3?
- Planar
- Hamiltonian
- Semi-planar
- Non-planar
-
For which smallest value of n does the complete graph Kn break the planar edge bound e ≤ 3n - 6?
- 3
- 4
- 6
- 5
-
What maximum number of edges can a simple planar graph with 7 vertices have?
- 14
- 15
- 21
- 16
-
What maximum number of edges can a simple planar bipartite graph with 10 vertices have?
- 20
- 24
- 16
- 26
-
According to Kuratowski's theorem, a graph is non-planar if it contains a subdivision of which graph?
- K3,3 or K4,4
- K5 or K3,3
- K5 or K4,4
- K4 or K2,3
-
How many entries equal 1 in the adjacency matrix of the complete graph K4?
- 4
- 16
- 12
- 6
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