Hi I understand that for rooted tree, the definition is as follow:
- Is a directed graph $D=<V,E>$
- $\exists v\in V\rightarrow \deg^-(v)=0$ which indicate the in-degree of $v$ is $0$
- $\forall v'\in(V/\{v\})\rightarrow\deg^-(v')=1$ which indicate the in-degree of nodes other than $v$ is $1$
I understand that an ordered tree is based on a rooted tree, which all sub-nodes of any node have an order. But I cannot find a formal mathematical expression for this.
May I ask how should I define it with formal mathematical expression??