LaTeX
|V|-|E|+|F|=2Variables
- V: vertices
- E: edges
- F: faces including the outer face
How to use this formula
Relates vertices, edges, and faces in a connected planar embedding.
Important notes
- The graph must be connected and planar in the chosen embedding.
- For c components, the right side becomes 1+c.
Quick example
A cube graph has 8−12+6=2.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The graph must be connected and planar in the chosen embedding.
- State whether the graph is directed, weighted, simple, connected, or finite whenever the formula depends on those properties.
Worked example
A cube graph has 8−12+6=2.
Common mistakes
- Before substituting values into Euler Formula for Planar Graphs, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Verify the result of Euler Formula for Planar Graphs with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Euler Formula for Planar Graphs 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
|V|-|E|+|F|=2. - 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 Euler Formula for Planar Graphs used for?
Relates vertices, edges, and faces in a connected planar embedding.
Can I copy this formula as LaTeX?
Yes. Copy |V|-|E|+|F|=2 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.