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I am trying to find the all the minimum spanning trees in the graph using kruskal's algorithm.

I know that if all the weight of the edges that is distinct from each other, there will only be one minimum spanning tree in the graph. So, for more than two minimum spanning tree in the graph, there must be at least two edges that has the same weight. Therefore, I am thinking I should start cutting the edges with the same amount of weight.

However, I am wondering will it make a difference if I cut different amount of edges at a time?

Thank you!!

Sirius
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If your graph has different edges with the same weight then you will have a choice on which edge to cut first, whichever ones you choose to cut first will give still give you a minimum spanning tree, but cutting in different order may give you different minimum spanning tree (though they'll all still have the same total weight).

However, I am wondering will it make a difference if I cut different amount of edges at a time?

You're not making sense, you can only cut one edge at a time with Kruskall.

Lie Ryan
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  • Are you indicating that to find the total amount of minimum spanning trees, I only have to cut one edge at a time? Also I don't understand why I can only cut one edge? I may cut two edges from the graph and generate another MST, right? Thanks. – Sirius Nov 08 '13 at 15:40