Understanding Factorials and Graph Theory

What is the factorial of 4?

• 12

• 32

• 24

• 16

What is the factorial of zero defined as?

• 10

• Undefined

• 1

• 0

What is the double factorial of 7?

• 420

• 105

• 210

• 315

How does the double factorial of an even number differ from that of an odd number?

• It skips odd numbers

• It includes all numbers up to the number itself

• It skips even numbers

• It is always zero

What is the double factorial of 8?

• 512

• 128

• 384

• 256

In graph theory, what are the basic components of a graph?

• Points and paths

• Nodes and lines

• Vertices and edges

• Dots and lines

What is a complete graph?

• A graph with no vertices

• A graph with no edges

• A graph with only one vertex

• A graph with all possible edges

What is a perfect matching in a graph?

• A matching where all vertices are connected to themselves

• A matching where every vertex is connected to exactly one other vertex

• A matching with no edges

• A matching with all vertices connected to one vertex

How many perfect matchings does a complete graph with an even number of vertices have?

• n squared

• n double factorial

• n factorial

• n cubed

What is the notation for a complete graph on n vertices?

• P_n

• K_n

• C_n

• G_n