## → History

**Graph Theory** was introduced by the famous Swiss mathematician named **Leonhard Euler**, to solve many mathematical problems by constructing graphs based on given data or a set of points.

• The graphical representation shows different types of data in the form of bar graphs, frequency tables, line graphs, circle graphs, line plots, etc.

## → Introduction to Graph:

**Graph **is a discrete structure consisting of vertices and edges connecting the vertices.

• It is used to create a pairwise relationship between objects.

## → Definition of Graph Theory:

**Graph Theory** is the study of points and lines. **In Mathematics**, it is a sub-field that deals with the study of graphs.

• It is a pictorial representation that represents the Mathematical truth.

• It is the study of relationship between the vertices (nodes) and edges (lines).

**» Formally, a graph is denoted as a pair G(V, E)**.

Where **V **represents the finite set **vertices **and **E **represents the finite set **edges**.

• Therefore, we can say a graph includes non-empty set of vertices V and set of edges E.

**Example****‣ **Suppose, **a Graph G=(V,E),**

where **Vertices**, V={a,b,c,d}**Edges**, E={{a,b},{a,c},{b,c},{c,d}}

## Simple Graph:

A graph G(V,E) is said to be simple if G has no loops and no parallel edges.

## Multigraph:

A graph will be known as a multi-graph if the same sets of vertices contain multiple edges. In this type of graph, we can form a minimum of one loop or more than one edge.

## Directed Graph:

A **directed graph**, or **digraph**, is a graph in which the edges have a direction. This means that each edge points from one vertex to another vertex.

## Undirected Graph:

An** undirected graph**, on the other hand, is a graph in which the edges do not have a direction. This means that each edge connects two vertices, but it does not matter which vertex the edge is pointing from.