Learning Objectives:

__Math Tutoring on Graph Theory__

In the modern world, planning efficient routes is essential for business and industry. The field of **Graph Theory** started nearly 300 years ago. The field of **Graph Theory** has exploded in importance in the last century, because of the growing complexity of business in a global economy and computational power that computers provide us.

*Some basic Graph Theory vocabulary which is used in math tutoring are as follows:*

**1. **** Graph:** A

**2. **** Vertex:** A

**3. ***Edge:***Edges** connects pairs of **vertices.** An edge can represent a physical connection between locations. Depending upon the problem being solved, sometimes **weights** are assigned to the **Edges.**

**4. ***Loop:*** **A** Loop** is a special type of edge that connects a **vertex**** **to itself. **Loops** are not used much in street network **graphs.**

**5. ***Valence:*** **The** ****Degree** or** ****Valence**** **of a vertex is the number of edges meeting at that **vertex.** It is possible for a **vertex** to have a degree of zero or larger.

**6. ***Path:*** **A** ****Path** is a sequence of **vertices** using the **edges.**

**7. ***Circuit:*** **A** ****Circuit**** **is a path that begins and ends at the same **vertex.**

**8. **** Connected Graph:** A graph is connected if there is a path from any

*Applications of Graph Theory:*

The application of **Graph Theory** is as varied as Product Distribution, laying new fiber optic lines for broadband internet, suggesting new friends within social network websites etc.

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**Hook questions:**

*1. **What is Graph Theory?*

*2. **Regarding Graph Theory define the followings:*

*Graph, Vertex, Edges, Loop, Degree, Path, Circuit, Connected Graph.*

*3. **State some applications of Graph Theory.*

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