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→ 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.

Suppose, a Graph G=(V,E),

image 96

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.

WhatsApp Image 2023 09 30 at 13.05.08 4fec4d34


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.

WhatsApp Image 2023 09 30 at 13.05.09 6c0a71f6

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.

image 163

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.

image 164

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