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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Verified Answer
An undirected graph G has n nodes. Its adjacency matrix is given by an...
If all non diagonal elements are 1, then every vertex is connected to every other vertex in the graph with an edge of weight 1. Such a graph has multiple distinct MSTs with cost n-1.
Most Upvoted Answer
An undirected graph G has n nodes. Its adjacency matrix is given by an...
X n matrix A = (a_{ij}), where a_{ij} = 1 if there is an edge between nodes i and j, and a_{ij} = 0 otherwise.
To find the degree of a node i in the graph G, we need to count the number of edges incident to node i. This can be done by summing the elements in the i-th row of the adjacency matrix A.
The degree of node i is given by the sum of the i-th row of the adjacency matrix A, which can be computed as:
deg(i) = ∑_{j=1}^{n} a_{ij}
where ∑ denotes the sum, and a_{ij} denotes the element in the i-th row and j-th column of the adjacency matrix A.
In other words, the degree of node i is equal to the sum of all the elements in the i-th row of the adjacency matrix A.
To find the degree of a node i in the graph G, we need to count the number of edges incident to node i. This can be done by summing the elements in the i-th row of the adjacency matrix A.
The degree of node i is given by the sum of the i-th row of the adjacency matrix A, which can be computed as:
deg(i) = ∑_{j=1}^{n} a_{ij}
where ∑ denotes the sum, and a_{ij} denotes the element in the i-th row and j-th column of the adjacency matrix A.
In other words, the degree of node i is equal to the sum of all the elements in the i-th row of the adjacency matrix A.
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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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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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
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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