Spectral graph theory - Research Paper Example

In this paper I will examine the facts and the new developments of graph theory with the use of the theoretical proofs laid forward by Fermat’s Little Theorem. In addition, I will also examine Nielson-Schreier’s point of view as far as the subject is concerned (Bonchev, Danail and Rouvray, 17). I will also discuss the concept’s new application to DNA arrangement and computer network security and its important application when it comes to the vertex cover graphs (Beineke, Lowell and Robin 69).

There is also the use of edge color and matching in development of vertex colouring and this has well been explained in y work. Graph theory is very fast gaining merits in the field of mathematics as a result of its application in other different fields such as computer science, biochemistry, and biotechnology (Cvetković & Dragoš, 21). This field make use important concept that are procedures related to a part of graph theory referred to as matching which in turn its results are used to prove Dilworth’s series disintegration theorem (Bonchev, Danail and Rouvray, 196).

One of the most ackn owledged field in graph theory is matching. Matching give an explanation that there is a set of left and right co-set agent of a subgroup and this can be seen in a finite group which in turn plays a viatl role in proving Dharwadker’s four-color theorem. In addition to this prove, there was also proof of existence of a subset of real numbers that could not be measured going with the views of Lebesgue. What we realize is that the theorem could also be proofed with the use of discrete mathematics (Beineke, Lowell and Robin 95).

A graph is said to be a cluster of dots linked together by lines and below is an example of such graph depicting the linked dots. However, this definition is not accurate enough to be used in mathematical arguments. In a conventional way a graph is suppose to be depicted as a pair of sets (V, E) in which V represents a