Definitions Exam 3

Question 1

The total number of vertices in a map is equal to twice the number of edges

Answer 1

False

Question 2

A path that starts at once vertex and goes through every other vertex exactly once is a Hamiltonian path.

Answer 2

True

Question 3

Each edge in map is in the boundary of exactly one face

Answer 3

False

Question 4

A path that starts at one vertex and goes through every other vertex exactly once is an Eulerian path

Answer 4

False

Question 5

The number of vertices in a dual map is the same as the number of vertices in the original map

Answer 5

False

Question 6

The number of vertices in a dual map is the same as the number of faces in the orginal map.

Answer 6

True

Question 7

It is possible for two maps with the same underlying graph to be different

Answer 7

True

Question 8

The underlying graph for a map must be connected

Answer 8

True

Question 9

If a connected graph has an Eulerian path, then it has either zero or two vertices of odd degree

Answer 9

True

Question 10

A path that starts at one vertex and goes through every edge exactly once is a Hamiltonian path

Answer 10

False

Question 11

The valence of a face is the number of edges in the map that are in the edge cycle of the face

Answer 11

True

Question 12

A path that starts at one vertex and goes through every edge exactly once is an Eulerian path

Answer 12

True

Question 13

If a connected graph has exactly two vertices of odd degree, then it has an Eulerian path

Answer 13

True

Question 14

It is possible to have a Regular map with the common face valence of 3 and common vertex valence of 3.

Answer 14

True

Question 15

The valence of a vertex is the number of edges in a graph that are connected to a vertex

Answer 15

True

Question 16

It is not possible for two maps with the same underlying graph to be different

Answer 16

False

Question 17

A map is called Regular if all vertices have the same valence and all faces of the same valence

Answer 17

True

Question 18

The face valence list in a dual map is the same as the face valence list in the original map

Answer 18

False

Question 19

If a graph has two vertices of odd degree, then it has an Eulerian circuit.

Answer 19

False

Question 20

Each edge in a map is in the boundary of exactly two faces

Answer 20

True

Question 21

It is possible to have a Regular map with the common face valence of 4 and common vertex valence of 5.

Answer 21

False

Question 22

A map is called regular if the vertex valence list is the same as the face valence list.

Answer 22

False

Question 23

A map is called regular if the vertex valence list is the same as the face valence list.

Answer 23

False

Question 24

It is possible to have a Regular map with the common face valence of 3 and common vertex valence of 5.

Answer 24

True

Question 25

If a connected graph has a Hamiltonian circuit, then it has either zero or two vertices of odd degree.

Answer 25

False

Question 26

The valence of a face is the number of vertices in the map that are in the boundary of the face

Answer 26

False