LaTeX
|E|=|V|-1Variables
- V: vertex set
- E: edge set
How to use this formula
States the edge count of a finite connected acyclic graph.
Important notes
- The formula characterizes trees among connected simple graphs.
- A forest with c components has |E|=|V|-c.
Quick example
A tree with 12 vertices has 11 edges.
Applicability, worked calculation, and verification
Assumptions and domain checks
- A forest with c components has |E|=|V|-c.
- State whether the graph is directed, weighted, simple, connected, or finite whenever the formula depends on those properties.
Worked example
A tree with 12 vertices has 11 edges.
Common mistakes
- Before substituting values into Tree Edge Count, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Verify the result of Tree Edge Count with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Tree Edge Count 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
|E|=|V|-1. - 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 Tree Edge Count used for?
States the edge count of a finite connected acyclic graph.
Can I copy this formula as LaTeX?
Yes. Copy |E|=|V|-1 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.