DOUBT ON MINIMAL SPANNING TREE

Question

II.  if an edge (u,v) is contained in some minimum spanning tree, then it is a light edge crossing some cut of the graph.

III. If (u,v) is a light edge connecting CC(connected component) to some other component in the forest of graph G, then (u, v) is     included in the minimum spanning tree.

 

didn’t understand the part “light edge crossing some cut of the graph”

can someone explain me with the diagram ??

Comments

those two statement are equivalent, right ?

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yup

but I couldn't  analyze the part  " it is a light edge crossing some cut of the graph."

what's that mean ?

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" it is a light edge crossing some cut of the graph."

means, it is minimum weight edge among those edges which are in the connecting other component

in e1,e2,e3 we should include one edge in any case which is should having less weight

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got it !

thanks @Shaik