Let $G$ be a weighted graph with edge weights greater than one and $G'$ be the graph constructed by squaring the weights of edges in $G$. Let $T$ and $T'$ be the minimum spanning trees of $G$ and $G'$, respectively, with total weights $t$ and $t'$. Which of the following statements is TRUE?
I think t' can never equal to t2. Lets a, b, c be the edge weights of MST of T. So, if T = T', then cost of MST of T = a+b+c, and cost of MST of T'=a2+b2+c2. Now, (a+b+c)2 ≠ a2+b2+c2, Unless a=b=c=1.
None of the above would mean all others are false rt? Or the question should have asked "Always TRUE". Here is the answer key same file as published by IIT-K.
This official site supposedly still has the key. But as usual no words for IIT IT department.
in case of multiple min spanning tree also. t > t2 and T=T'.
I don't understand your 3rd point. Could u explain? @pragya
@ Pragy Agarwal Sir, How option C can be true.. Please give an example... Even in case of multiple MSTs, although T and T' may be different but still t' will not be equal to t2 in any case. Please clarify
we can make different as well as same MST also so option (d) is correct option