Edges And Vertices Of Graph - Tutorialspoint

• Home
• Whiteboard
• Online Compilers
• Practice
• Articles
• AI Assistant
• Jobs
• Tools
• Corporate Training
• Courses
• Certifications

Menu Categories Login

• Switch theme

• SQL
• HTML
• CSS
• Javascript
• Python
• Java
• C
• C++
• PHP
• Scala
• C#
• Tailwind CSS
• Node.js
• MySQL
• MongoDB
• PL/SQL
• Swift
• Bootstrap
• R
• Machine Learning
• Blockchain
• Angular
• React Native
• Computer Fundamentals
• Compiler Design
• Operating System
• Data Structure and Algorithms
• Computer Network
• DBMS
• Excel

• Data Structure
• Networking
• RDBMS
• Operating System
• Java
• MS Excel
• iOS
• HTML
• CSS
• Android
• Python
• C Programming
• C++
• C#
• MongoDB
• MySQL
• Javascript
• PHP

• Selected Reading
• UPSC IAS Exams Notes
• Developer's Best Practices
• Questions and Answers
• Effective Resume Writing
• HR Interview Questions
• Computer Glossary
• Who is Who

Edges and Vertices of Graph MathematicsComputer EngineeringMCA

A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges. The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.

Graph Theory

Definition − A graph (denoted as G = (V, E)) consists of a non-empty set of vertices or nodes V and a set of edges E. A vertex a  represents an endpoint of an edge. An edge joins two vertices a, b  and is represented by set of vertices it connects.

Example − Let us consider, a Graph is G = (V, E) where V = {a, b, c, d} and E = {{a, b}, {a, c}, {b, c}, {c, d}}

Here V is verteces and a, b, c, d are various vertex of the graph.

Here E represents edges and {a, b}, {a, c}, {b, c}, {c, d} are various edge of the graph.

Degree of a Vertex − The degree of a vertex V of a graph G (denoted by deg (V)) is the number of edges incident with the vertex V.

Vertex	Degree	Even / Odd
a	2	even
b	2	even
c	3	odd
d	1	odd

Even and Odd Vertex − If the degree of a vertex is even, the vertex is called an even vertex and if the degree of a vertex is odd, the vertex is called an odd vertex.

Degree of a Graph − The degree of a graph is the largest vertex degree of that graph. For the above graph the degree of the graph is 3.

The Handshaking Lemma − In a graph, the sum of all the degrees of all the vertices is equal to twice the number of edges. For example, in above case, sum of all the degrees of all vertices is 8 and total edges are 4.

Mahesh Parahar Updated on: 2019-08-23T07:19:16+05:30

31K+ Views

Kickstart Your Career

Get certified by completing the course

Get Started Print Page Previous Next Advertisements