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Let G be a complete undirected graph of six vertices. If the vertices of G are labelled, then the number of distinct cycles of length 4 in G is
Correct answer is '45'. Can you explain this answer?
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Let G be a complete undirected graph of six vertices. If the vertices ...
There can be total 6C4 ways to pick four vertices from six. The value of 6C4 is 15.
Note that the given graph is complete, so any four vertices can form a cycle.
There can be six different cycles with four vertices. For example, consider four vertices a, b, c and d.
(a, b, c, d, a)
(a, b, d, c, a)
(a, c, b, d, a)
(a, c, d, b, a)
(a, d, b, c, a)
(a, d, c, b, a)
And (a, b, c, d, a) and (a, d, c, b, a); (a, b, d, c, a) and (a, c, d, b, a); and (a, c, b, d, a) and (a, d, b, c, a) are same cycles.
So, total number of distinct cycles = (15 x 3) = 45
Note that the given graph is complete, so any four vertices can form a cycle.
There can be six different cycles with four vertices. For example, consider four vertices a, b, c and d.
(a, b, c, d, a)
(a, b, d, c, a)
(a, c, b, d, a)
(a, c, d, b, a)
(a, d, b, c, a)
(a, d, c, b, a)
And (a, b, c, d, a) and (a, d, c, b, a); (a, b, d, c, a) and (a, c, d, b, a); and (a, c, b, d, a) and (a, d, b, c, a) are same cycles.
So, total number of distinct cycles = (15 x 3) = 45
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Let G be a complete undirected graph of six vertices. If the vertices of G are labelled, then the number of distinct cycles of length 4 in G isCorrect answer is '45'. Can you explain this answer?
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Let G be a complete undirected graph of six vertices. If the vertices of G are labelled, then the number of distinct cycles of length 4 in G isCorrect answer is '45'. 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 Let G be a complete undirected graph of six vertices. If the vertices of G are labelled, then the number of distinct cycles of length 4 in G isCorrect answer is '45'. 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 Let G be a complete undirected graph of six vertices. If the vertices of G are labelled, then the number of distinct cycles of length 4 in G isCorrect answer is '45'. Can you explain this answer?.
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