Course Solutions Uncategorized (Solved) : Following Statements May May Correct Case Either Prove Correct Give Counterexample Correct Q32043109 . . . .

(Solved) : Following Statements May May Correct Case Either Prove Correct Give Counterexample Correct Q32043109 . . . .

June 27, 2024June 27, 2024| adminadmin| 0 Comment| 8:10 pm
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The following statements may or may not be correct. In each case, either prove it (if it is correct) or give a counterexample (if it is not correct). Always assume that the graph G = (V,E) is undirected, connected and the edge weights are positive. (5 points eac) (a) If a graph G has more than V 1 edges, and there is a unique heaviest edge, then this edge cannot be part of a MST (b) If G has a cycle with a unique heaviest edge e, then e cannot be part of an MST. (c) Let e be any edge of minimum weight in G. Then e must be part of some MST (d) If the lightest edge in a graph is unique, then it must be part of every MST. (e) The shortest path tree computed by Dijkstras is necessarily an MST

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