Graph Components are Equivalence Classes
From ProofWiki
Theorem
The components of a graph are equivalence classes under the relation is connected to on the set of vertices.
Proof
We have that Graph Connectedness is an Equivalence Relation.
The result follows directly from the definition of component.
$\blacksquare$
Sources
- Gary Chartrand: Introductory Graph Theory (1977): $\S 2.3$: Problem $44$
