A tree is a connected graph which contains no cycles. This means that there is exactly one path between any two vertices.
When an edge is added to a tree this always creates a cycle (provided no vertex is added as well) When an edge is removed from a tree the resulting graph is no longer connected (again, provided no vertex was removed).
A tree is
These are some invariant values for trees with vertices:
Invariant name | Invariant value |
---|---|
Size | |
Clique number | 1, when 2 in all other cases |