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Trees

Terms in this set (34)

What is a tree?
a connected simple graph with no simple cycles
What are the properties of a tree?
1. there is a unique simple path between any 2 of a tree's vertices
2. If we add an edge to a tree, it creates a cycle
3. If we remove an edge from a tree, it becomes not connected
What are some examples of trees?
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What is a rooted tree?
a tree in which one vertex has been designated as the root.
We can change an unrooted tree to a rooted tree by choosing any vertex as the root
When are 2 rooted trees isomorphic?
Two rooted trees are isomorphic if there is a bijection between their vertices that:
take the root to root &
take edges to edges & non-edges to non-edges
When is a vertex a parent of another vertex?
If vertices u & v are connected by an edge & u is closer to the root than v (above v) then u is the parent of v & v is a child of u
When are vertices siblings?
vertices have the same parent
What is a leaf?
a childless vertex
What is an internal vertex?
vertices with at least 1 child
What are ancestors?
The ancestors of a non-root vertex v are the vertices in the (unique) simple path from the root to v
What are descendants?
The descendants of vertex v are the vertices that have v as an ancestor
What is an example of the basic terminology?
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What are some of the applications of trees?
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What is the level of a vertex?
the length of the (unique) path from the root to v
What is the height of a rooted tree?
The height of a rooted tree is the maximum of the levels of its vertices
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