# IISc CSA - Research Interview Question

180 views
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$
0

@ankitgupta.1729

just taking 2 regular of 4 vertex we can prove it

rt??

2
If in IISc let's let's meet infront of CSA department at 5.
0

I am not there,I havenot got that chance

might be there

1
what a question by professor !

Beautiful merging of 2 concepts :)
1

@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

0
So we have to use like mathematical induction ? or soem other concept ?
1
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

## Related questions

1 vote
1
303 views
A proper vertex colouring of a graph $G$ is a colouring of the vertices in $G$ in such a way that two vertices get different colours if they are adjacent. The minimum number of colours required for proper vertex colouring of $G$ is called the chromatic number of $G$. Then what is the chromatic number of the cycle graph on 149 vertices?
What is the determinant of the following matrix? $\begin{matrix} 76 && 18 && 34 \\ 14 && 12 && 6 \\ 90 && 30 && 40 \end{matrix}$
Which of the following statement(s) is(are) true? If $n$ is odd prime number then $2^{n-1} \text{ mod } n =1$ If $2^{n-1} \text{ mod } n =1$ for a number $n$ then $n$ is prime