Ace Test series: Graph Theory - Graph Connectivity

Question

Please can anyone tell whether my answer is wrong or solution provided by them is correct??

Comments

172 is correct.

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They're asking for minimum number of edges that should be 19.. why you are giving answer as 172?.. they are not mentioning graph is complete..

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see the word 'necessarily connected', with 19 edges you can not guarantee necessarily connected condition

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thanks @nitish

Answer 1

Your Answer is Correct .
They had Provided Wrong Solution . And in formula it is > not >= .

$\Rightarrow $ With $171$ edges $19$ vertices can connect completely i.e $K_{19}$

$\Rightarrow \therefore 172$ ensures connection of $20^{th}$ vertex.