Which of the following is false?

A graph with one odd vertex will have an Euler Path but not an Euler Circuit.

Euler Paths exist when there are exactly two vertices of odd degree.

Euler circuits exist when the degree of all vertices are even.

A graph with more than two odd vertices will never have an Euler Path or Circuit.

A given graph has vertices with the given degrees: 3, 5, 6, 8, 2 What is DEFINITELY TRUE?

This graph will be a Euler's Path

This graph will be a Euler's Curcuit

This graph will be a Hamiltonian Path

A graph has the vertices with the following degrees: 4, 6, 8, 2, 2, 6, 4 What do we DEFINITELY KNOW?

This will have a Euler's Circuit

This will have a Hamiltonian Path

Hamilton Paths and Circuits

Authored by Staci Smith

Mathematics

9th - 12th Grade

CCSS covered

Used 229+ times

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which of the following is a Hamilton circuit of the graph?

ABCDEFGA

ACBEGFDA

CBGEDFAC

CEGBADFC

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

List a path from vertex D to vertex G

DAFCEBG

DFACEBG

DECAFBG

DCBAFEG

MULTIPLE CHOICE QUESTION

1 min • 1 pt

True or false: With Hamilton circuits, every edge must be used. With Euler circuits, every vertex must be used.

True

False

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

How many distinct Hamilton circuits are there in this complete graph? (There is a formula for this)

120

What is the cost using Nearest Neighbor (Go Cheap) starting with vertex A?

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find a Hamilton circuit from D using the Nearest Neighbor Alogrithm.

DAEBCD

DBEACD

DABECD

DCABED

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

How would you rewrite the circuit AEDBCA where B is the starting vertex?

BEDCAB

BCAEDB

BACEDB

BADECB

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Hamilton Paths and Circuits

Which of the following is a Hamilton circuit of the graph?

List a path from vertex D to vertex G

True or false: With Hamilton circuits, every edge must be used. With Euler circuits, every vertex must be used.

How many distinct Hamilton circuits are there in this complete graph? (There is a formula for this)

What is the cost using Nearest Neighbor (Go Cheap) starting with vertex A?

Find a Hamilton circuit from D using the Nearest Neighbor Alogrithm.

How would you rewrite the circuit AEDBCA where B is the starting vertex?

How many edges are there in the complete graph K₉?

How many distinct hamilton circuits are possible in the complete graph K₁₁?

Using the Brute Force method (Exhaustive Search), find the optimal route.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Hamilton Paths and Circuits

Which of the following is a Hamilton circuit of the graph?

List a path from vertex D to vertex G

True or false: With Hamilton circuits, every edge must be used. With Euler circuits, every vertex must be used.

How many distinct Hamilton circuits are there in this complete graph? (There is a formula for this)

What is the cost using Nearest Neighbor (Go Cheap) starting with vertex A?

Find a Hamilton circuit from D using the Nearest Neighbor Alogrithm.

How would you rewrite the circuit AEDBCA where B is the starting vertex?

How many edges are there in the complete graph K9?

How many distinct hamilton circuits are possible in the complete graph K11?

Using the Brute Force method (Exhaustive Search), find the optimal route.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

How many edges are there in the complete graph K₉?

How many distinct hamilton circuits are possible in the complete graph K₁₁?