Choose a minimum-total-weight tree connecting every vertex of a finite graph. Beside minimum spanning tree, the output shows the operation used to obtain it.
Kruskal’s method selects A-B, C-D, and B-C in the sample for total weight 4.
A minimum spanning tree connects all vertices without cycles while minimizing the sum of selected edge weights.
Use Vertices for the first Minimum Spanning Tree reasonableness check. Then use Weighted edges to test whether the scale and direction of Minimum Spanning Tree follow the stated rule.
It designs low-cost cables, roads, pipelines, clusters, and network backbones. Minimum Spanning Tree also relates to required edge count.
Disconnected graphs have no spanning tree, and tied weights can produce several equally optimal trees.
Compare the result with the worked example's scale before relying on the reported minimum spanning tree.
The cleanest input audit is to restate the problem using vertices and weighted edges. If that sentence sounds wrong, correct the assignment before asking for minimum spanning tree.
Decreasing an unused edge can make it enter the optimal tree and displace another edge. The pattern also provides a quick estimate of whether a revised result is plausible.
The formula and result serve different readers: the formula shows what was done, and the rounded minimum spanning tree communicates scale. Keep both when the work needs review.
Dijkstra minimizes a single route, not the total cost of connecting every vertex. The wording of the problem should decide which operation is appropriate.
A screenshot is unnecessary when the shown formula and the supplied inputs (vertices and weighted edges) are saved in plain text. Include the input convention if the reported Minimum Spanning Tree classification will be reused.
The selected result needs exactly |V|−1 edges, no cycle, full coverage, and the displayed total weight.
Sort edges by weight, add each unless it closes a cycle, and stop after |V|−1 selections. Minimum Spanning Tree also connects to route objective.
A minimum spanning tree connects all vertices without cycles while minimizing the sum of selected edge weights.
It designs low-cost cables, roads, pipelines, clusters, and network backbones.
Disconnected graphs have no spanning tree, and tied weights can produce several equally optimal trees.
Sort edges by weight, add each unless it closes a cycle, and stop after |V|−1 selections.