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- 1. Multiple ChoiceTracing all edges on a figure without picking up your pencil or repeating and starting and stopping at different spotsEuler CircuitEuler Path
- 2. Multiple ChoiceEuler paths must touchall edgesall vertices
- 3. Multiple Choice
Does this graph have an Euler Path, Euler Circuit, both, or neither?Euler PathEuler CircuitBothNeither - 4. Multiple ChoiceThis graph will have a Euler's Path.TrueFalse
- 5. Multiple ChoiceDoes this graph have a Euler's Path?TrueFalse
- 6. Multiple Choice
Is the following graph complete?
Yes
No
- 7. Multiple Choice
In the graph above, which of the following statements is true?
A is adjacent to E
A is not adjacent to D
C is adjacent to D
C is not adjacent to E
- 8. Multiple Choice
Using the following tournament information, construct a directed graph and find a ranking of the participants:
Between A and B, A wins
Between A and C, C wins
Between A and D, D wins
Between B and C, C wins
Between B and D, D wins
Between C and D, C wins
1st place: A, 2nd place: B, 3rd place: C, 4th place: D
1st place: B, 2nd place: A, 3rd place: D, 4th place: C
1st place: C, 2nd place: D, 3rd place: A, 4th place: B
1st place: D, 2nd place: C, 3rd place: B, 4th place: A
- 9. Multiple Choice
In how many colors can you color this picture, following the rules of the 4 color theorem?
1
2
3
4
- 10. Multiple Choice
What is the chromatic number of the graph?
1
2
3
4
- 11. Multiple Choice
Allie's bridesmaids are throwing her a bridal shower in a month, and they have several tasks to complete beforehand. The tasks, times and prerequisites are organized in the chart above. Will they finish in time, if the month is 30 days long?
Yes, and they will have 4 days to spare.
No, they will be 4 days late.
Yes, they will be exactly on time.
Yes, and they will have 17 days to spare.
- 12. Multiple Choice
A bipartite graph has two distinct groups where ...
All vertices in Group 1 are connected to all vertices of Group 2
No Vertices in either group connecting to members of their own group
contains no isolated vertices
must have members of Group 1 above the members of Group 2
- 13. Multiple ChoiceCircuits start and stop atsame vertexdifferent vertices
- 14. Multiple Choice
Vertex
a line connecting two vertices
a point
an edge
an edge that starts and ends at the same vertex
- 15. Multiple Choice
Adjacent vertices
are connected to every other vertex in the graph
are connected by at least one edge
are in a loop together
make a multigraph
- 16. Multiple Choice
A loop is when
there is a path going from a vertex back to itself
An edge that starts and ends at the same vertex
if it were removed, the graph would be disconnected
connects two vertices to each other
- 17. Multiple Choice
A path is
an edge that starts and ends at the same vertex
a connection between two vertices
a series of consecutive edges in which no edge is repeated
a complete graph
- 18. Multiple Choice
A graph is connected if
Each vertex can reach any other vertex
each vertex is adjacent to every other vertex
All the vertices are odd
the length of all the edges are equal
- 19. Multiple Choice
A graph is complete if
every vertex is adjacent to every other vertex
it contains at least one loop
it has an Euler path
it has an Euler circuit
- 20. Multiple Choice
The degree of a vertex is
also called the order or valence
the number of loops
is the number of edges that connect to that vertex
how many times it can be part of a path
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