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Theorem 6.2.4 If T is a graph on n vertices, then the following statements are equivalent. 1. T is a tree. 2. T is connected and has n- 1 edges. 3. T is acyclic and has n - 1 edges. 4. T is connected, but the deletion of any edge disconnects the graph.

Theorem 6.2.4 If T is a graph on n vertices, then the following statements are equivalent. 1. T is a tree. 2. T is connected and has n- 1 edges. 3. T is acyclic and has n - 1 edges. 4. T is connected, but the deletion of any edge disconnects the graph.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 33EQ
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Theorem 6.2.4 If T is a graph on n vertices, then the following statements are equivalent. 1. T is a tree. 2. T is connected and has n- 1 edges. 3. T is acyclic and has n - 1 edges. 4. T is connected, but the deletion of any edge disconnects the graph.
Transcribed Image Text:Theorem 6.2.4 If T is a graph on n vertices, then the following statements are equivalent. 1. T is a tree. 2. T is connected and has n- 1 edges. 3. T is acyclic and has n - 1 edges. 4. T is connected, but the deletion of any edge disconnects the graph.
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