Mathematics Quiz Discrete

Question 1

1 / 1 pts

Suppose you have an endorelation on a set. If you turned that endorelation into a graph, you would always find that the degree of each vertex must be less than the cardinality of the set.

Correct!

True

False

Question 2

0 / 1 pts

If you represented a symmetric relation as a graph, what feature(s) would that graph be guaranteed to have? Check all that apply.

The graph would be weighted.

The graph would be directed.

You Answered

The graph would be unweighted.

Correct!

The graph would be undirected.

The graph would be connected.

The graph would be disconnected.

The graph would have at least one cycle.

The graph would not have any cycles.

Question 3

Original Score: 1 / 1 pts

If two vertices in a graph are connected, that means they have an edge between them.

True

Correct!

False

Question 4

1 / 1 pts

All graphs have at least one edge.

True

Correct!

False

Question 5

1 / 1 pts

If you have a free tree, adding any additional edge to it makes it no longer a free tree.

Correct!

True

False

Question 6

1 / 1 pts

If you have a free tree, removing any edge from it makes it no longer a free tree.

Correct!

True

False

Question 7

0 / 1 pts

The set of all rooted trees is a subset of the set of all binary search trees.

You Answered

True

False

Question 8

1 / 1 pts

All graphs are connected graphs.

True

Correct!

False

Question 9

1 / 1 pts

Suppose you had a free tree, and turned it into a rooted tree. It would have the same height no matter which node you chose to make the root.

True

Correct!

False

Question 10

1 / 1 pts

The leaves of a (rooted) tree will always be at the same depth.

True

Correct!

False

Question 11

1 / 1 pts

Every node in a (rooted) tree will always have exactly one parent, except the root, which never has a parent.

Correct!

True

False

Question 12

1 / 1 pts

On Twitter, a user can “follow” another user without being followed in return. (For instance, I follow R pioneer and statistician Hadley Wickham, but he is way too famous to follow me.) Also, when you “follow” someone, you just plain follow them — you don’t “super follow” them, or “barely follow” them.

Is the Twitter graph (where users are vertices, and edges represent “followings” between users) a directed or undirected graph? And is it weighted or unweighted?

directed and weighted

Correct!

directed and unweighted

undirected and weighted

undirected and unweighted

Question 13

Original Score: 1 / 1 pts Regraded Score: 1 / 1 pts

This question has been regraded.

A website called Ubermapquest has a giant GIS graph of all vehicular intersections in all seven continents of the world. (Not really, but pretend.) This graph has information about how many kilometers are between each vehicular intersection, and whether the route between them is traversable in both directions or only one. (For instance, in downtown Fredericksburg, you can drive directly on a one-way street from Caroline & William to Caroline & Amelia, but not the other way.)

Is the Ubermapquest graph (where vertices are intersections, and edges are driveable paths between them) directed or undirected? Is it weighted or unweighted? Is it connected or disconnected?

directed, weighted, and connected

Correct!

directed, weighted, and disconnected

directed, unweighted, and connected

directed, unweighted, and disconnected

undirected, weighted, and connected

undirected, weighted, and disconnected

undirected, unweighted, and connected

undirected, unweighted, and disconnected

Question 14

0 / 3 pts

What is the total distance of all the edges in the minimal spanning tree of the graph below?

You Answered

Correct Answers

36.0 (with margin: 0.0)

Question 15

1.5 / 1.5 pts

What order would the nodes in the following binary tree be visited if it were traversed in pre-order? (Type the letters as capitals, with no spaces or other punctuation, like this: SWAGDEYHUP. That’s not the actual correct answer, of course.)