Question:Question 1 options:

A ______is a collection of vertices (at least one) and edges.Each edge goes from one vertex to another.

Question 2 options:

Two graphs are_____if there is a one-to-one matching between vertices of the two graphs with the property that whenever there is an edge between two vertices of either graph, there is an edge between the corresponding vertices of the other graph.

Question 3 options:

A graph is_______

if we can move from each vertex of the graph to every other vertex of the graph along edges of the graph.

Question 4

Connected pieces of a graph are called components of the graph.

True

False

Question 5

The number of edges joined to a vertex is called the

isomorphism of the vertex.

component of the vertex.

degree of the vertex.

edge of the vertex.

Question 6

In any graph, the sumof the degrees of the vertices equals the number of edges.

True

False

Match the term with its definition.

Question 7 options:

a sequence of vertices, each linked to the next vertex by a specified edge of the graph such that no edge is used more than once.

a sequence of vertices, each linked to the next vertex by a specified edge of the graph such that no edge is used more than once and beginning and ending at the same vertex.

a sequence of vertices, each linked to the next vertex by a specified edge of the graph.

1)Walk

2)Path

3)circuit

Question 8

Aconnected graphis a graph in which there is exactly one edge going from each vertext to each other vertex.

True

False

Question 9

A graph consisting of some of the vertices of th original graph and some of the original edges between those vertices is called a

.

Question 10

In both Euler paths and Euler circuits, every edge of the graph is used at least once.

True

False

Question 11

Which of the following is one part of Euler's Theorem?

If a connected graph has an Euler circuit, then each vertex has even degree.

If a connected graph has an Euler circuit, then each vertex has odd degree.

If a disconnected graph has an Euler circuit, then each vertex hasodd degree.

If a graph has an Euler circuit, then each vertex has even degree.

Question 12

A cut edge in a graph is an edge whose removal disconnects a

of the graph.

Question 13

Fleury's algorithm is usedfor finding an Euler circuit in a connected graph in whch each vertex has even degree.

True

False

Question 14

A graph that has an Euler Circuit will only have one Euler Circuit.

True

False

Question 15

Decide whether the statement is true or false.

A graph containing one or more vertices of degree 1 can have an Euler circuit.

True

False