Graph Optimization and Edge Duplication

Graph Optimization and Edge Duplication

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to determine if a graph has an Euler circuit using Euler's theorem, which states that a graph has an Euler circuit if all vertices have even degrees. If not, the graph can be modified by duplicating existing edges to achieve even degrees for all vertices. The process involves analyzing vertex degrees, identifying odd degrees, and strategically duplicating edges to ensure all vertices have even degrees, thus creating an Euler circuit.

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16 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main problem discussed in the video?

Calculating the total number of edges in a graph

Determining if a graph is connected

Finding the shortest path in a graph

Determining if a graph has an Euler circuit

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

According to Euler's theorem, when does a graph have an Euler circuit?

When all vertices have odd degrees

When all vertices have even degrees

When the graph is a tree

When the graph is complete

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the degree of a vertex?

The number of edges connected to the vertex

The number of loops in the graph

The number of vertices in the graph

The number of paths through the vertex

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many vertices with odd degrees are initially present in the graph?

Five

Three

Two

Four

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the degree of vertex B before any edge duplication?

4

1

2

3

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in optimizing a graph with vertices of odd degrees?

Changing vertex labels

Duplicating existing edges

Removing edges

Adding new vertices

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which edge is duplicated first in the example to reduce odd degree vertices?

Edge from C to F

Edge from E to G

Edge from A to B

Edge from B to D

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