Essays on Graph Theory

A new model for controlling traffic in urban has been proposed. The main aim is to use the system to maximize the network throughput and use its signals to meet the changing traffic demand. It is modeled as a Discrete Event System (DES).It has sensors, observers and a controller. These models support the off-line planning of vehicles, traffic lights setting and road networks. It has signals that detect the arrival and departure of vehicles. The controller controls how the vehicles arrive and depart.

The model also represents behavioral conflicts. Two vehicles may attempt to occupy the same zone. In ...

Forewords

Discrete mathematics discovers its applications in the contemporary era of computer science. Every component of discrete mathematics is extensity used in computer science. In this reflective paper, graph theory will be focused in the context of its applications. A graph is a modeling tool or set of relationships and technically stating it is a set of vertices and edges in which the graph theory is used as a modeling tool to study the network designs, communications and structure designs. Graph theory ideas are extensity utilized in computer science. It helps in a different area of research as image segmentation,data mining, clustering, ...

1.0 Introduction Many sports played across the world that involves throwing, hitting and kicking are done so using a ball. However, many parameters such as humidity, materials of manufacture of the ball, size of the ball, etc. control the movement of the ball in air. Research on golf balls and tennis balls reveal their aerodynamic properties and the various parameters affecting their flight. The effect of seams on a baseball on the flight has been evaluated along with the relationship between rotation and lateral forces (Watts & Sawyer 1987). Similar studies have also been conducted on cricket balls, rugby balls, volleyballs ...

The Graph below represents a map of Manhattan and four surrounding land masses with bridges and tunnels connecting to Manhattan.

Key NJ- New Jersey LT-Lincoln Tunnel M-Manhattan BBT- Brooklyn Battery tunnel BR- Brooklyn BB- Brooklyn Bridge B- Bronx WB-Williamsburgh Bridge Q-Queens QMT-Queens Midtown Tunnel QB-Queensbrough Bridge WAB-Willis Avenue Bridge TB-Triborough Bridge TAB- Third Avenue Bridge GW- George Washington Bridge HT-Holland Tunnel - The degree of a vertex implies the number of edges joined to that vertex.

The degrees of vertices in the Graph above are as follows are:

- Vertex M is of degree 13 - Vertex B is of degree 4 - Vertex Br is of degree 4 - Vertex Q is of degree 4 - Vertex NJ ...