 ## Tutoring on Graph Theory

Learning Objectives:

#### Understand and apply Graph Theory

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 Graph is a finite set of dots and connecting links. The dots are called vertices or nodes and the links are called edges. A Graph can be used to simplify a real life model and is the basic structure used in Graph Theory.

2.  Vertex: A Vertex or Node is a dot in the graph where edges meet.

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 vertex to any other vertex.

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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