Let $=(,,)$

be a connected weighted graph in which each edge $$ in $$

has weight $()>0$

$.$ Suppose $1$

is a Shortest Path Tree $($SPT$)$ of $$

rooted at some source vertex $$

$,$ and $2$

is a Minimum Spanning Tree $($MST$)$ of $$

$.$ Now consider keeping the same set of vertices and edges, but modifying the edge weights to get a modified graph $=(,,)$

$,$ where the modified edge weights are defined as $()=(4+())(7+())$

$,$ for each edge $$ in $$

$.$

Then, as a set of edges in $$

$,$