DM_12 - Discrete Mathematics(CSC 1204 10.1 Introduction to Trees 1 What is a Tree Definition A tree is a connected undirected graph with no simple

DM_12 - Discrete Mathematics(CSC 1204 10.1 Introduction to...

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Discrete Mathematics (CSC 1204) 10.1 Introduction to Trees 1
What is a Tree? 2
Example 1 (p.683)Which of the graphs shown in Figure 2 are trees? 3
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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 Tree a b c d e f g a b c d e f g Once a vertex of a tree has been designated as the root of 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

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