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Let G = ( V , E , w ) be a connected weighted graph in which each edge e in E has weight w
Let GVEw
be a connected weighted graph in which each edge e in E
has weight we
Suppose T
is a Shortest Path Tree SPT of G
rooted at some source vertex s
and T
is a Minimum Spanning Tree MST of G
Now consider keeping the same set of vertices and edges, but modifying the edge weights to get a modified graph GVEw
where the modified edge weights are defined as wewew
for each edge e in E
Then, as a set of edges in G
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