Why is T not a minimum spanning tree of G? The Problem: Let T be a tree constructed by Dijkstra's algorithm in the process of solving the single source shortest-paths problem for a weighted connected graph G.
   &nbsp;   &nbsp;a. True of false: T is a spanning tree of G?
   &nbsp;    &nbsp;b. True of false: T is a minimum spanning tree of G?

I read from Single source shortest paths problem  is a problem  "in which we have to find shortest paths from a source vertex v to all other vertices in the graph."  I read from Partial Solutions that only one of the options is true.

From my intution and the statements above, I reasoned that a is true while b is false. This is because if T is a minimum spanning tree of G, be definition it should also be a spanning tree of G. I am trying to show that b is false with a counterexample but I can't find/draw a graph in which T isn't a min spanning tree.

Can anyone show me a counterexample to b? To me, Dijkstra's algorithm is similar to Prim's algorithm to find MSt, so in the end T should be a min spanning tree.
Vertices: {A,B,C}

Edges: (undirected)
{A,B,4}
{A,C,3}
{B,C,2}

So basically it's a triangle with the given weights. Starting from A, Dijkstra's algorithm will give you (A,B) and (A,C) but the minimum spanning Tree will give you (A,C) and (C,B).