

Planar Graphs and Euler's Formula
Interactive Video
•
Mathematics, Science
•
9th - 12th Grade
•
Practice Problem
•
Hard
Sophia Harris
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a planar graph?
A connected graph that can be drawn without any edges crossing
A graph that can be drawn with edges crossing
A graph that cannot be drawn without edges crossing
A disconnected graph with no edges
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How many faces does a planar graph have if it is drawn without edges crossing?
The number of faces is always five
The number of faces is always the same
The number of faces can change with different drawings
The number of faces is always two
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What must be true to accurately count the number of faces in a graph?
The graph must be drawn in a planar way
The graph must be drawn with edges crossing
The graph must be disconnected
The graph must have more vertices than edges
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does Euler's formula relate in a connected planar graph?
The number of vertices, edges, and faces
The number of vertices and edges only
The number of vertices and faces only
The number of edges and faces only
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
According to Euler's formula, what is the result of V - E + F for a connected planar graph?
0
1
3
2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the value of V - E + F when a new vertex and edge are added to a planar graph?
It increases by 1
It decreases by 1
It remains the same
It doubles
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the effect on V - E + F when a new edge is added between two existing vertices in a planar graph?
It remains the same
It decreases by 1
It increases by 1
It becomes negative
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