# Week 1 > Warm Up Flashcards

1

Q

What is a Graph?

A

- A set of objects 2. Relations between pairs of objects 3. A Graph G = (V, E)

2

Q

u and v are End Points of e

A

3

Q

What is the incident of Graph?

A

u and e are Incident

4

Q

Draw adjacent u and v vertices

A

5

Q

**Objects: {A,B,C,D}****Relations: {{A,C},{D,A},{B,D},{C,B}}**

A

6

Q

**What is the Directed Graph?**

**Draw:** Objects: {A,B,C,D} A C B D Relations: {(A,C),(D,A),(B,D),(C,B)}

A

- It is often convenient to consider Directed Edges (Arcs)
- They describe asymmetric relations
- There is a flight from A to B, but not the other way around

7

Q

**Are these graphs the same?**

A

Yes, both have 10 vertices and 15 edges

8

Q

What is the degree of a vertex?

A

9

Q

What is the degree of the graph?

A

10

Q

Find the degree of a vertex

A

**The degree of v is 6: deg(v) 6****The degree of v**_{6 }is 1: deg(v_{6}) = 1

11

Q

**What are the isolated vertices?**

**deg(v**_{<span>2</span>}) = ?**deg(v**_{8}) = ?**deg(v**_{0}) = ?

A

**deg(v**_{<span>2</span>}) = 2**deg(v**_{8}) = 1**deg(v**_{0}) = 0

Thus, **v _{0 }is isolated vertice.**

12

Q

- What is the regular graph?
- Is the graph is a regular graph?

A

- See attached
- Yes, since each vertex has the same degree

13

Q

- What is the complement graph?

A

14

Q

A

15

Q

Can you complement of graph?

A

16

Q

What are Graph Paths?

A