How can we compute the shortest-path tree of minimum total weight for a given connected graph?I am using Dijkstra's algorithm to find the shortest-path tree, but there may exist more than one shortest-path tree with different total weights.The above picture shows one such example (where $a$ represents the starting vertex).Is there a way to find the shortest-path tree of minimum total weight without inspecting every possible shortest-path tree?
Minimum-weight shortest-path tree
algorithms;graphs;graph theory;trees;shortest path