Graph Theory

is the study of relationships, providing a helpful tool to quantify and simplify the moving parts of a dynamic system.

• Graph Theory

• Mathematical Modeling

• Graph Modeling

• Graph Relationship

Graph theory was first introduced in the 18th century by the Swiss mathematician

• Leonhard Euler

• Leonhardt Euler

• Leonhard Ruler

• Leonhardt Ruler

The city of K¨onigsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the _______

• Pregel River

• Prehel River

• Prussian River

• Kneiphof River

We think of a ______ as a set of points in a plane or in 3-space and a set of line segments (possibly curved), each of which either joins two points or joins a point to itself

• Graph

• Model

• Line

• Drawings

is a mathematical structure consisting of two finite sets V and E.

• Graph

• Model

• Line

• Drawings

The elements of V are called ______ (or nodes)

• Graph

• Vertices

• Edge

• Endpoints

the elements of E are called ______

• Graph

• Vertices

• Edge

• Endpoints

Each edge has a set of one or two vertices associated to it, which are called its _____

• Graph

• Vertices

• Edge

• Endpoints

is said to join its endpoints

• Graph

• Vertices

• Edge

• Endpoints

The ________ of a vertex v in a graph G, denoted N(v), is the set of all the neighbors of v.

• Open Neighborhood

• Closed Neighborhood