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An undirected graph C 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 l’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?
Verified Answer
An undirected graph C has n nodes. Its adjacency matrix is given by a...
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. See the below example.
The connected graph:
Below are three Minimum Spanning trees each of cost 2.0.
Minimum Spanning Tree 1
Minimum Spanning Tree 2
Minimum Spanning Tree 3
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An undirected graph C 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 l’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?
Question Description
An undirected graph C 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 l’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 GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An undirected graph C 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 l’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 GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An undirected graph C 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 l’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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