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An undirected graph G which is connected and acyclic is called ____________
- a)bipartite graph
- b)cyclic graph
- c)tree
- d)forest
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
An undirected graph G which is connected and acyclic is called _______...
An undirected graph G which is connected and acyclic is termed as a tree. G contains no cycles and if any edge is added to G a simple cycle is formed.
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An undirected graph G which is connected and acyclic is called _______...
Connected and Acyclic Graph
- A connected graph is a graph in which there is a path between every pair of vertices.
- An acyclic graph is a graph that does not contain any cycles or closed loops.
Definition of a Tree
- A tree is a connected and acyclic graph.
- Therefore, when a graph is both connected and acyclic, it is called a tree.
Characteristics of a Tree
- In a tree, there is exactly one path between any two vertices.
- A tree with n vertices will have exactly n-1 edges.
- Removing any edge from a tree will disconnect the graph.
Therefore, in the context of the question, an undirected graph G that is connected and acyclic is called a tree. This terminology is used because trees exhibit these specific characteristics in graph theory.
- A connected graph is a graph in which there is a path between every pair of vertices.
- An acyclic graph is a graph that does not contain any cycles or closed loops.
Definition of a Tree
- A tree is a connected and acyclic graph.
- Therefore, when a graph is both connected and acyclic, it is called a tree.
Characteristics of a Tree
- In a tree, there is exactly one path between any two vertices.
- A tree with n vertices will have exactly n-1 edges.
- Removing any edge from a tree will disconnect the graph.
Therefore, in the context of the question, an undirected graph G that is connected and acyclic is called a tree. This terminology is used because trees exhibit these specific characteristics in graph theory.
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