Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Consider the following statements regarding t...
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Consider the following statements regarding trees:
1. A tree contains all the nodes of the graph.
2. A tree shall contain any one of the loops.
3. Every connected graph has at least one tree.
Which of the above statements are correct?
- a)1 and 2 only
- b)1 and 3 only
- c)2 and 3 only
- d)1, 2 and 3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider the following statements regarding trees:1. A tree contains a...
The Correct Answer is Option B: 1 and 3 only.
Explanation:
Let's analyze each statement one by one to determine their correctness.
Statement 1: A tree contains all the nodes of the graph.
This statement is correct. A tree is a type of graph that is connected and acyclic, which means it does not contain any loops or cycles. In a tree, every node is connected to every other node through a unique path. Therefore, all the nodes in a graph must be present in a tree.
Statement 2: A tree shall contain any one of the loops.
This statement is incorrect. As mentioned earlier, a tree is a graph without any loops or cycles. Therefore, a tree cannot contain any loops. If a graph contains a loop, it cannot be considered a tree.
Statement 3: Every connected graph has at least one tree.
This statement is correct. A connected graph is a graph in which there is a path between any two nodes. To form a tree from a connected graph, we need to remove some edges to eliminate any loops or cycles. By removing a minimum number of edges, we can obtain a tree that preserves the connectivity of the original graph. Therefore, every connected graph can be transformed into at least one tree.
Based on the analysis of each statement, we can conclude that statements 1 and 3 are correct, while statement 2 is incorrect. Thus, the correct answer is option B: 1 and 3 only.
Explanation:
Let's analyze each statement one by one to determine their correctness.
Statement 1: A tree contains all the nodes of the graph.
This statement is correct. A tree is a type of graph that is connected and acyclic, which means it does not contain any loops or cycles. In a tree, every node is connected to every other node through a unique path. Therefore, all the nodes in a graph must be present in a tree.
Statement 2: A tree shall contain any one of the loops.
This statement is incorrect. As mentioned earlier, a tree is a graph without any loops or cycles. Therefore, a tree cannot contain any loops. If a graph contains a loop, it cannot be considered a tree.
Statement 3: Every connected graph has at least one tree.
This statement is correct. A connected graph is a graph in which there is a path between any two nodes. To form a tree from a connected graph, we need to remove some edges to eliminate any loops or cycles. By removing a minimum number of edges, we can obtain a tree that preserves the connectivity of the original graph. Therefore, every connected graph can be transformed into at least one tree.
Based on the analysis of each statement, we can conclude that statements 1 and 3 are correct, while statement 2 is incorrect. Thus, the correct answer is option B: 1 and 3 only.
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Community Answer
Consider the following statements regarding trees:1. A tree contains a...
Let us consider the following electric circuit:
An equivalent graph corresponding to the above electric circuit is shown in the following figure:
Tree:
The tree is a connected subgraph of a given graph, which contains all the nodes of a graph. But, there should not be any loop in that subgraph. The branches of a tree are called as twigs.
This connected subgraph contains all the four nodes of the given graph and there is no loop.
Hence, it is a Tree.
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