Trees

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 nameInvariant value
Size
Clique number1, when
2 in all other cases