May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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11-2 Discrete Mathematical Structures
11.1.1 Definition
A graph is acyclic if it has no cycles. A tree is a connected acyclic graph.
11.1.2 Properties of Tree
1. There is one and only one path between every pair of vertices of a tree.
2. If in a graph G, there is one and only one path between every pair of vertices, then G is a
tree.
3. A tree with n vertices has (n - 1) edges.
4. Any connected graph with n vertices and (n - 1) edges is a tree.
5. A graph is a tree if and only if it is minimally connected.
6. In any tree with two or more vertices, there are at least two pendant vertices.
Examples
1. The genealogy of a family is represented ...
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