LaTeX
\sum_{v\in V}\deg(v)=2|E|Variables
- V: vertex set
- E: edge set
- deg(v): degree of vertex v
How to use this formula
Relates the sum of all vertex degrees in a finite undirected graph to twice its edge count.
Important notes
- Every edge contributes one to the degree of each endpoint.
- The number of odd-degree vertices is therefore even.
Quick example
For degrees 3, 2, 2, 1, the sum is 8, so the graph has 4 edges.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Every edge contributes one to the degree of each endpoint.
- For the Handshake Lemma, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- State whether the graph is directed, weighted, simple, connected, or finite whenever the formula depends on those properties.
Worked example
For degrees 3, 2, 2, 1, the sum is 8, so the graph has 4 edges.
Common mistakes
- Do not omit the index or bounds in Handshake Lemma; changing either one changes which terms are included.
- Verify the result of Handshake Lemma with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Handshake Lemma in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\sum_{v\in V}\deg(v)=2|E|. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Handshake Lemma used for?
Relates the sum of all vertex degrees in a finite undirected graph to twice its edge count.
Can I copy this formula as LaTeX?
Yes. Copy \sum_{v\in V}\deg(v)=2|E| or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.