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Which of the following statements about trees is correct?
- a)A tree is a connected acyclic graph.
- b)A tree is a directed graph with no cycles.
- c)A tree is a graph with no loops and no multiple edges.
- d)A tree is a graph with no loops but may have multiple edges.
Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements about trees is correct?a)A tree is a...
A tree is a non-linear data structure consisting of nodes connected by edges. It has a hierarchical structure with a root node and children nodes.
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Which of the following statements about trees is correct?a)A tree is a...
Answer:
Introduction:
In graph theory, a tree is a type of graph that is widely used in various applications. It is a collection of nodes (vertices) connected by edges. Trees have several properties that distinguish them from other types of graphs.
Definition of a Tree:
A tree is a connected acyclic graph. This means that a tree is a graph where every pair of nodes is connected by a unique path and there are no cycles or loops in the graph. In other words, there is only one path between any two nodes in a tree, and it is impossible to start at a node and return to it by following the edges.
Explanation of Correct Answer:
Option 'A' states that a tree is a connected acyclic graph, which is the correct definition of a tree. Let's break down the statement to understand why it is correct:
1. Connected: A tree is a connected graph, meaning that there is a path between every pair of nodes. This ensures that the graph is not divided into disconnected components.
2. Acyclic: A tree is an acyclic graph, meaning that it does not contain any cycles or loops. This ensures that there are no paths that start and end at the same node without visiting any other node in between.
Explanation of Incorrect Options:
Let's briefly explain why the other options are incorrect:
- Option 'B': A tree is not necessarily a directed graph. It can be either directed or undirected, depending on the specific application or problem.
- Option 'C': A tree can have multiple edges between nodes, but it cannot have loops or cycles. So, this statement is incorrect.
- Option 'D': A tree cannot have loops, but it can have multiple edges between nodes. Therefore, this statement is also incorrect.
Conclusion:
In summary, a tree is a connected acyclic graph, which means it is a graph with no cycles or loops. This definition distinguishes trees from other types of graphs and makes them useful in various applications, such as data structures, network analysis, and algorithm design.
Introduction:
In graph theory, a tree is a type of graph that is widely used in various applications. It is a collection of nodes (vertices) connected by edges. Trees have several properties that distinguish them from other types of graphs.
Definition of a Tree:
A tree is a connected acyclic graph. This means that a tree is a graph where every pair of nodes is connected by a unique path and there are no cycles or loops in the graph. In other words, there is only one path between any two nodes in a tree, and it is impossible to start at a node and return to it by following the edges.
Explanation of Correct Answer:
Option 'A' states that a tree is a connected acyclic graph, which is the correct definition of a tree. Let's break down the statement to understand why it is correct:
1. Connected: A tree is a connected graph, meaning that there is a path between every pair of nodes. This ensures that the graph is not divided into disconnected components.
2. Acyclic: A tree is an acyclic graph, meaning that it does not contain any cycles or loops. This ensures that there are no paths that start and end at the same node without visiting any other node in between.
Explanation of Incorrect Options:
Let's briefly explain why the other options are incorrect:
- Option 'B': A tree is not necessarily a directed graph. It can be either directed or undirected, depending on the specific application or problem.
- Option 'C': A tree can have multiple edges between nodes, but it cannot have loops or cycles. So, this statement is incorrect.
- Option 'D': A tree cannot have loops, but it can have multiple edges between nodes. Therefore, this statement is also incorrect.
Conclusion:
In summary, a tree is a connected acyclic graph, which means it is a graph with no cycles or loops. This definition distinguishes trees from other types of graphs and makes them useful in various applications, such as data structures, network analysis, and algorithm design.
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Which of the following statements about trees is correct?a)A tree is a connected acyclic graph.b)A tree is a directed graph with no cycles.c)A tree is a graph with no loops and no multiple edges.d)A tree is a graph with no loops but may have multiple edges.Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements about trees is correct?a)A tree is a connected acyclic graph.b)A tree is a directed graph with no cycles.c)A tree is a graph with no loops and no multiple edges.d)A tree is a graph with no loops but may have multiple edges.Correct answer is option 'A'. Can you explain this answer? for Software Development 2024 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Which of the following statements about trees is correct?a)A tree is a connected acyclic graph.b)A tree is a directed graph with no cycles.c)A tree is a graph with no loops and no multiple edges.d)A tree is a graph with no loops but may have multiple edges.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Software Development 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements about trees is correct?a)A tree is a connected acyclic graph.b)A tree is a directed graph with no cycles.c)A tree is a graph with no loops and no multiple edges.d)A tree is a graph with no loops but may have multiple edges.Correct answer is option 'A'. Can you explain this answer?.
Which of the following statements about trees is correct?a)A tree is a connected acyclic graph.b)A tree is a directed graph with no cycles.c)A tree is a graph with no loops and no multiple edges.d)A tree is a graph with no loops but may have multiple edges.Correct answer is option 'A'. Can you explain this answer? for Software Development 2024 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about Which of the following statements about trees is correct?a)A tree is a connected acyclic graph.b)A tree is a directed graph with no cycles.c)A tree is a graph with no loops and no multiple edges.d)A tree is a graph with no loops but may have multiple edges.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Software Development 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements about trees is correct?a)A tree is a connected acyclic graph.b)A tree is a directed graph with no cycles.c)A tree is a graph with no loops and no multiple edges.d)A tree is a graph with no loops but may have multiple edges.Correct answer is option 'A'. Can you explain this answer?.
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