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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?
(A) $T' = T$ with total weight $t' = t^2 $
(B) $T' = T$ with total weight $t' < t^2$
(C) $T' \neq T$ but total weight $t' = t2$
(D) None of the above
When the edge weights are squared the minimum spanning tree won't change.
$t'$ < $t^2$, because sum of squares is always less than the square of the sums except for a single element case.
Hence, B is the general answer and A is also true for a single edge graph. Hence, in GATE 2012, marks were given to all.
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?
(A) $T' = T$ with total weight $t' = t^2 $
(B) $T' = T$ with total weight $t' < t^2$
(C) $T' \neq T$ but total weight $t' = t2$
(D) None of the above
When the edge weights are squared the minimum spanning tree won't change.
$t'$ < $t^2$, because sum of squares is always less than the square of the sums except for a single element case.
Hence, B is the general answer and A is also true for a single edge graph. Hence, in GATE 2012, marks were given to all.
GATECSE