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
C is false with this graph
we can make different as well as same MST also so option (d) is correct option
It's a test series conducted by Kiran sir i.e...