We have undirected weighted connective graph $G=(V,E)$, We also have a minimum spanning tree $T$ of $G$. Let $v$ be some vertex. We have new graphs, $G'$ and $T'$. $G'$ and $T'$ are same $G$ and $T$, except the extra node $v$ witch is connected (with new weighted edges) to the same nodes in both graphs. I need to prove that $G'$ MSP has the same weight as $T'$ MSP. I was thinking about using kruskal or prim algorithm to show that Given a MSP of $T'$, We can use kruskal or prim on $G'$ to find it, with no results.