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What is Graph and Graph Theory?

Graph

A graph is a pictorial and mathematical representation of a set of objects where some pairs of objects are connected by links.

The interconnected objects are represented by points termed as vertices or nodes and the links that connect the vertices are called edges or arcs or lines.

In other words, a graph is an ordered pair G = (V, E) where,

• G specifies the graph.
• V is the vertex-set whose elements are called the vertices, or nodes of the graph. This set is often denoted by V(G) or just V.
• E is the edge-set whose elements are called the edges, or connections between vertices of the graph. This set is often denoted by E(G) or just E.

Let’s see the following graph:

In the above graph,

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Graph Theory

Graph theory is the sub-field of mathematics and computer science which deals with graphs, diagrams that contain points and lines and which often pictorially represents mathematical truths.

In short, graph theory is the study of the relationship between edges and vertices.