Algebraic Properties of Graphs : A study

Abstract

Algebraic 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.