100%(5)5 out of 5 people found this document helpful
This preview shows page 1 - 11 out of 30 pages.
Discrete Mathematics(CSC 1204) 10.1 Introduction to Trees1
What is a Tree?2
Example 1 (p.683)•Which of the graphs shown in Figure 2 are trees?3
Theorem 1•An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.5
Rooted Tree•Rooted tree: A rooted tree is a tree in which one vertex has been designated as the root and every edge is directed away from the root.7
Rooted TreeabcdefgabcdefgOnce a vertex of a tree has been designated as the rootof the tree, it is possible to assign direction to each of the edges.
Ordered Rooted Tree•Ordered rooted tree: An ordered rooted tree is a rooted tree where the children of each internal vertex are ordered.9
Tree Terminologies•Parent: Suppose T is a rooted tree. If v is a vertex in T other than the root, the parent of v is the unique vertex u such that there is a directed edge from u to v –Note that such a vertex is unique•Child