A study of Graph Theory, its characteristics and applications

Abstract

Algebric graph theory is that branch of graph theory where algebraic techniques are used to study graphs. In this branch, properties about graph are being translated into algebraic properties and then by making use of algebraic methods, theorems on graphs are deduced. The widely applied part of algebra to graph theory is linear algebra comprising of the theory of matrices and linear vector spaces. A graph is completely determined either by its adjacencies or incidences. This information can be conveniently stated in the matrix form.
A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense “related”. The objects of the graph correspond to vertices and the relations between them correspond to edges. A graph is depicted diagrammatically as a set of dots depicting vertices connected by lines or curves depicting edges. Formally, “A graph G = (V,E) consists of V, a non-empty set of vertices (or nodes) and E, a set of edges. Each edge has either one or two vertices associated with it, called its endpoints.”