→ 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.
Thank you for reading this post, don't forget to subscribe!• 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.
