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Tree and Forest in Graph Theorem | Theorem 9.1 in chapter 4 (Trees) || Book Robin J. Wilson
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In this video we define Trees and Forest in Graph theory Also we discuss their related theorem
Theorem 9.1
Let T be Graph with n vertices. Then the following statements are equivalent.
1- T be a tree
2- T contains no cycle, and has n-1 edges
3- T is connected and has n-1 edges
4- T is connected and each edge is a bridge
5- any two vertices of T are connected by exactly one path
6- T contains no cycle but the addition of any edge creates exactly one cycle
#Theorem9.1
#Tree&Forest
Theorem 9.1
Let T be Graph with n vertices. Then the following statements are equivalent.
1- T be a tree
2- T contains no cycle, and has n-1 edges
3- T is connected and has n-1 edges
4- T is connected and each edge is a bridge
5- any two vertices of T are connected by exactly one path
6- T contains no cycle but the addition of any edge creates exactly one cycle
#Theorem9.1
#Tree&Forest
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