Understanding Planar Graphs

Understanding Planar Graphs

University

10 Qs

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Understanding Planar Graphs

Understanding Planar Graphs

Assessment

Quiz

Mathematics

University

Practice Problem

Hard

Created by

Dr.Nagaveni K

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a planar graph?

A graph that can only be drawn in three dimensions.

A graph that contains no vertices.

A graph where all edges must intersect.

A graph that can be drawn on a plane without edges crossing.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following graphs is planar: K5, K3,3, or a triangle?

square

K3,3

triangle

K5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Can a graph with 5 vertices and 10 edges be planar?

It depends on the graph structure

No

Yes

Yes, if it has no cycles

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the maximum number of edges in a planar graph with n vertices?

4n - 8

2n - 4

3n - 6

n^2 - n

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Is every tree a planar graph? Why or why not?

Only some trees are planar graphs depending on their structure.

No, trees can have crossings that make them non-planar.

Yes, every tree is a planar graph.

Trees are always non-planar due to their branching nature.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can you determine if a graph is non-planar?

A graph is non-planar if it contains a subgraph that is a subdivision of K5 or K3,3.

A graph is non-planar if it contains a cycle of length 4.

A graph is non-planar if it has more than 10 vertices.

A graph is non-planar if it is colored with more than 3 colors.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is Kuratowski's theorem in relation to planar graphs?

A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 or K3,3.

A finite graph is planar if it has no cycles.

A finite graph is planar if and only if it contains a subgraph that is a subdivision of K3,3.

A finite graph is planar if it contains a subgraph that is a subdivision of K5.

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