A Study on Graph and Its Approaches

Exploring the Fundamentals of Graph Theory

Abstract

The theory of graphs is one of the few fields ofmathematics with a definite birth date. Graph theory is considered to havebegun in 1736 with the publication of Euler’s solution of the Konigsberg bridgeproblem. Any mathematical object involving points and connections between themmay be called a graph. A graph G consists of a nonempty set V (G) of objectscalled vertices and a (possibly empty) set E(G) of two element subsets of V(G), called edges. The set V (G) is called the vertex set of G and E(G) itsedge set. The number of vertices in a graph G is called its order, and thenumber of edges is its size. A graph of order p and size q is called a (p,q)-graph.