# Minimum Distance Spanning Tree Dijkstra

I would like to construct a Minimum Distance Spanning Tree (Dijkstra) for the graph below:

MDST: {(a,c), (c,h), (c,f), (a,d), (h,g), (a,b), (d,e), (h,j), (h,i), (j,k), (e,m), (i,l)}

Is my understanding correct? The total cost would be 49 (sum of the distance from the root for each node).

• I think you are confusing MST with the shortest path problem. The two most common MST algorithms are Kruskal and Prim's algorithms that already work on weighted graphs. Dijkstra algorithm, whereas calculates the shortest distance from one to all. – kelalaka Dec 10 '18 at 17:50

What you are computing is typically called a shortest-path tree; yours is rooted at $$a$$. Note that, in this example, the shortest-path tree rooted at $$a$$ is not unique. You could have taken the edge $$(d, e)$$ instead of $$(a, e)$$.