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Consider the following statements regarding the degree of the vertex in graph G.
S1: The number of odd degree vertices is always even in every graph G.
S2: In every simple undirected graph, at least 2 vertices must have the same degree.
S3: Every bipartite graph is bichromatic.
The number of true statements are _______.
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the following statements regarding the degree of the vertex ...
S1 is quite popular and easy to understand.
S2 however, is actually a corollary of the Havel-Hakimi Theorem, which says, there exists no graphical sequence with all distinct degrees.
S3 is also true, as every bipartite graph can be coloured using exactly 2 colours.
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Consider the following statements regarding the degree of the vertex in graph G.S1: The number of odd degree vertices is always even in every graph G.S2: In every simple undirected graph, at least 2 vertices must have the same degree.S3: Every bipartite graph is bichromatic.The number of true statements are _______.a)2b)3c)4d)1Correct answer is option 'B'. Can you explain this answer?
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Consider the following statements regarding the degree of the vertex in graph G.S1: The number of odd degree vertices is always even in every graph G.S2: In every simple undirected graph, at least 2 vertices must have the same degree.S3: Every bipartite graph is bichromatic.The number of true statements are _______.a)2b)3c)4d)1Correct answer is option 'B'. 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 Consider the following statements regarding the degree of the vertex in graph G.S1: The number of odd degree vertices is always even in every graph G.S2: In every simple undirected graph, at least 2 vertices must have the same degree.S3: Every bipartite graph is bichromatic.The number of true statements are _______.a)2b)3c)4d)1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements regarding the degree of the vertex in graph G.S1: The number of odd degree vertices is always even in every graph G.S2: In every simple undirected graph, at least 2 vertices must have the same degree.S3: Every bipartite graph is bichromatic.The number of true statements are _______.a)2b)3c)4d)1Correct answer is option 'B'. Can you explain this answer?.
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