IISc CSA - Research Interview Question

Question

Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$

Comments

@srestha mam, 

just taking 2 regular of 4 vertex we can prove it

 by taking examples we can not prove something... 

for saying something is false, we can use one example, but for saying something is true, we can't do like that

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So we have to use like mathematical induction ? or soem other concept ?

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yes....

taking any k-regular graph, i observed that, if we think in vector form, there are some vectors are repeating.

we are trying for rank, so by eliminating duplicates, i am getting as rank k.

Even this is also not formal proof