What is a minimum spanning tree in graph theory?
An example of an AI chatbot conversation about minimum spanning trees in graph theory.
What is a minimum spanning tree in graph theory?
A minimum spanning tree (MST) is a subset of edges in a connected, weighted graph that connects all vertices with the minimum possible total edge weight.
Can you explain how to find a minimum spanning tree?
Sure! Two popular algorithms to find an MST are Prim's algorithm and Kruskal's algorithm. Would you like a brief overview of each?
Yes, please explain Prim's algorithm.
Prim's algorithm starts with a single vertex and grows the MST by adding the smallest edge that connects a vertex in the tree to a vertex outside the tree.
What about Kruskal's algorithm?
Kruskal's algorithm sorts all edges by weight and adds them one by one to the MST, ensuring no cycles are formed until all vertices are connected.
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