number of cycles in given graph:

Question

Let N1 be the number of distinct cycles of length 3 in given graph and N2 be the number of distinct cycles of length 3, if the graph is labelled.

Then N2 - N1 is __________

Comments

out of 5 vertices we have to select 3 vertices to make a cyclw of lenght 3  So  5C3 for unlabbleled nodes

if nodes are labelled then 5C3 * 3   30 - 10 =20   

Am I rt????

Answer 1

There are total 10 triangles of length 3

unlabeled cycles :10(N1)

labeled cycle :3*10(N2)

N2-N1=30-10=20

Comments

what about 4 and 5 vertex cycle?

Can you checkout this and correct me?

https://gateoverflow.in/105343/how-many-maximum-cycles-possible-complete-graph-check-answer

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ur approach is absolutely correct!