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# What is graph theory?

Overview(graph theory)Graph theory is intimately related to many branches of mathematics. We widely use in subjects like, Computer Technology, Communication Science, Electrical Engineering, Physics, Architecture, Operations Research, Economics, Sociology, Genetics, etc..

It also has uses in social sciences, chemical sciences, information retrieval systems, linguistics even in economics also.

Graphs are discrete structures consisting of vertices and edges that connects these vertices.

There are several different types of graphs that differ with respect to the kind and number of edges that can a connect a pair of vertices.

## Basic terminology

Graph theory is a relatively new area of mathematics. Graph is the form of representing of descriptive data in the terms of verticals and edges. hence, we use Graph theory in various fields like computer science, information technology, genetics, telecommunication etc.

A graph is a collection of vertices and edges in which each edge is assigned to pair of points, we call them terminal.

Hence, we can say that a graph is a network of dots connect by lines.

Mathematically we can define a graph as-

A graph is a pair of set (V, E) where-

1. V is a non-empty set, we call its elements vertices.

2. E is collection of two-element subset of V, we call it edges.

Terminology: A graph G is an order pair (V, E) where V is a non-empty set and E is the set of edges in which each element of E is assign to a unique unorder pair of elements of V.

We denote an element of a set E as- e = (v, su) where u, v ∈ V.

hence, U and v are the end vertices of edge e.

Note- In any graph the number of vertices with odd degree must be even.

Loop: If both the end vertices of an edge are same then we call the edge as a loop.

Parallel edge: If two or more edges have same terminal vertices, then we call these edges as parallel edges.

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