Essays on Eulerian

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, ...

Travelling salesman problem is a grouped as a NP-hard problem. The problem involves identifying the shortest route that a sales man would follow to visit several cities. The travelling salesman problem model several problems of real life applications. There are approximations algorithms developed to solve the problem. However, an exact feasible solution to the general Travelling salesman problem has not been developed; although, the problem has been under research for more than half a decade. Small traveling salesman problems have been solved using exact algorithms developed through various methods, such as genetic algorithms. It has been proved that the TSP cannot be ...

Euler circuits

In a graph proposition, an Eulerian trail refers to a graph that moves to each edge precisely once. On the same note, Eulerian circuits (Eulerian cycle) refers to Eulerian trail that originates and stops on the one vertex. This was first applied by Leonard Euler whereby he stated that appropriate condition for the presence of Eulerian circuits is that the entire graph vertices have even level, and illustrated without confirming that joined graphs with having even degree entails Eulerian circuit. Euler tour within an undirected graph refers to a cycle, which applies every edge just once. When such a cycle is present, the ...