- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Sum of Degrees of Vertices Theorem
If G = (V, E) be a non-directed graph with vertices V = {V1, V2,…Vn} then
n ∑ i=1 deg(Vi) = 2|E|
Corollary 1
If G = (V, E) be a directed graph with vertices V = {V1, V2,…Vn}, then
n ∑ i=1 deg+(Vi) = |E| = n ∑ i=1 deg−(Vi)
Corollary 2
In any non-directed graph, the number of vertices with Odd degree is Even.
Corollary 3
In a non-directed graph, if the degree of each vertex is k, then
k|V| = 2|E|
Corollary 4
In a non-directed graph, if the degree of each vertex is at least k, then
k|V| = 2|E|
Corollary 5
In a non-directed graph, if the degree of each vertex is at most k, then
k|V| = 2|E|
Advertisements