Unique Tree of Order 2

From ProofWiki
Jump to navigation Jump to search

Theorem

There exists exactly one tree of order $2$:

Tree-Order-2.png


Proof

By definition, a graph of order $2$ has exactly $2$ nodes.

By Finite Connected Simple Graph is Tree iff Size is One Less than Order, such a tree has one edge.

There is trivially only one way to connect $2$ nodes with one edge.

Hence the result.

$\blacksquare$