Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > An undirected graph G has n nodes. Its adjace...
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An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?
- a)Graph G has no minimum spanning tree (MST)
- b)Graph G has a unique MST of cost n-1
- c)Graph G has multiple distinct MSTs, each of cost n-1
- d)Graph G has multiple spanning trees of different costs
Correct answer is option 'C'. Can you explain this answer?
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An undirected graph G has n nodes. Its adjacency matrix is given by an...
Explanation:
An undirected graph G with n nodes and adjacency matrix is given by an n x n square matrix whose (i) diagonal elements are 0s and (ii) non-diagonal elements are 1s.
To understand the solution, we need to understand the properties of an MST.
Properties of MST:
- An MST is a tree that connects all the vertices of the graph with the minimum possible total edge weight.
- An MST does not contain any cycles.
- An MST has n-1 edges, where n is the number of vertices in the graph.
Now let's analyze the given options:
a) Graph G has no minimum spanning tree (MST)
This option is incorrect because every connected graph has at least one spanning tree, and an MST is a spanning tree with the minimum possible total edge weight.
b) Graph G has a unique MST of cost n-1
This option is incorrect because the given graph has non-diagonal elements as 1s, which means every node is connected to every other node. Therefore, there can be multiple MSTs.
c) Graph G has multiple distinct MSTs, each of cost n-1
This option is correct because of the following reasons:
- The given graph is connected, so it has at least one spanning tree.
- All the non-diagonal elements of the adjacency matrix are 1s, which means every node is connected to every other node.
- As a result, there can be multiple MSTs, each of cost n-1, since all the edges have the same weight.
d) Graph G has multiple spanning trees of different costs
This option is incorrect because all the edges in the given graph have the same weight, i.e., 1. Therefore, all the MSTs will have the same cost, which is n-1.
Hence, the correct answer is option (c).
An undirected graph G with n nodes and adjacency matrix is given by an n x n square matrix whose (i) diagonal elements are 0s and (ii) non-diagonal elements are 1s.
To understand the solution, we need to understand the properties of an MST.
Properties of MST:
- An MST is a tree that connects all the vertices of the graph with the minimum possible total edge weight.
- An MST does not contain any cycles.
- An MST has n-1 edges, where n is the number of vertices in the graph.
Now let's analyze the given options:
a) Graph G has no minimum spanning tree (MST)
This option is incorrect because every connected graph has at least one spanning tree, and an MST is a spanning tree with the minimum possible total edge weight.
b) Graph G has a unique MST of cost n-1
This option is incorrect because the given graph has non-diagonal elements as 1s, which means every node is connected to every other node. Therefore, there can be multiple MSTs.
c) Graph G has multiple distinct MSTs, each of cost n-1
This option is correct because of the following reasons:
- The given graph is connected, so it has at least one spanning tree.
- All the non-diagonal elements of the adjacency matrix are 1s, which means every node is connected to every other node.
- As a result, there can be multiple MSTs, each of cost n-1, since all the edges have the same weight.
d) Graph G has multiple spanning trees of different costs
This option is incorrect because all the edges in the given graph have the same weight, i.e., 1. Therefore, all the MSTs will have the same cost, which is n-1.
Hence, the correct answer is option (c).
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An undirected graph G has n nodes. Its adjacency matrix is given by an...
An undirect graph g has node
n into n square matrices whose digonal
0,s and is graph g has multiple distinct MSTs, each of cost n-1 ans
n into n square matrices whose digonal
0,s and is graph g has multiple distinct MSTs, each of cost n-1 ans
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An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer?
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An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer?.
An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?a)Graph G has no minimum spanning tree (MST)b)Graph G has a unique MST of cost n-1c)Graph G has multiple distinct MSTs, each of cost n-1d)Graph G has multiple spanning trees of different costsCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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