This calculator helps you find the Minimum Spanning Tree (MST) of a graph using Kruskal's Algorithm. Ideal for students and professionals in graph theory, it solves the problem of connecting all vertices with the minimum total edge weight.
This tool relies on the standard Kruskal's Algorithm for computing the Minimum Spanning Tree. For more details, refer to authoritative sources such as textbooks on graph theory.
Using Kruskal's Algorithm, the graph's edges are sorted by weight, and the smallest edges are added to the MST until all nodes are connected without forming a cycle.
Consider a graph with nodes 1, 2, and 3, and edges (1,2,3), (2,3,4). Enter this data, and the calculator will find the MST by first sorting edges by weight, then using a union-find structure to ensure no cycles, and finally outputting the MST.
Kruskal's Algorithm is a greedy algorithm used to find the MST of a graph by sorting edges and adding them to the MST in order of increasing weight.
No, Kruskal's Algorithm is only applicable to undirected graphs.
A MST is a subset of edges connecting all nodes in a graph with the minimum possible total edge weight.
Cycles are avoided using a union-find data structure that tracks node connectivity.
It's efficient for sparse graphs and helps understand fundamental graph theory concepts.