- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- 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

# Sum of Degrees of Vertices Theorem

If G = (V, E) be a non-directed graph with vertices V = {V_{1}, V_{2},…V_{n}} then

n ∑ i=1 deg(V

_{i}) = 2|E|## Corollary 1

If G = (V, E) be a directed graph with vertices V = {V_{1}, V_{2},…V_{n}}, then

n ∑ i=1 deg

^{+}(V_{i}) = |E| = n ∑ i=1 deg^{−}(V_{i})## 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|

- Related Questions & Answers
- Maximize the sum of products of the degrees between any two vertices of the tree in C++
- Construct a graph from given degrees of all vertices in C++
- Check whether given degrees of vertices represent a Graph or Tree in Python
- Edges and Vertices of Graph
- Initial Value Theorem of Laplace Transform
- Final Value Theorem of Laplace Transform
- Initial Value Theorem of Z-Transform
- Final Value Theorem of Z-Transform
- Constant Flux Linkage Theorem of Synchronous Machines
- Program to find out the sum of minimum cost within a graph among all vertices in Python
- Area of a polygon with given n ordered vertices in C++
- Program find number of subsets of colorful vertices that meets given conditions in Python
- Return the angle of the complex argument in degrees in Python
- Get the Trigonometric sines of an array of angles given in degrees in Python
- Get the Trigonometric cosine of an array of angles given in degrees with Python

Advertisements