URGENT!
Posted: Fri Apr 29, 2022 6:34 am
URGENT!
Q4. Minimum Spanning Trees (MST) (15 points) State TRUE or FALSE. If FALSE, provide a counter-example: (a) if (u, v) is a minimum-edge in a connected graph G, then (u, v) belongs to some MST of G. [3 points) (b) There exists some connected graph such that the set of edges {(u, v): there exists a cut (S.V-S) such that (u, v) is a light edge crossing (S,V - S)} does not form an MST. (3 points) (c) The heaviest edge in a connected graph cannot belong to an MST. [3 points) (d) A graph where every edge weight is unique has a unique MST. (3 points) (e) Prim's and Kruskal's algorithms will always return the same MST. (3 points)
Q4. Minimum Spanning Trees (MST) (15 points) State TRUE or FALSE. If FALSE, provide a counter-example: (a) if (u, v) is a minimum-edge in a connected graph G, then (u, v) belongs to some MST of G. [3 points) (b) There exists some connected graph such that the set of edges {(u, v): there exists a cut (S.V-S) such that (u, v) is a light edge crossing (S,V - S)} does not form an MST. (3 points) (c) The heaviest edge in a connected graph cannot belong to an MST. [3 points) (d) A graph where every edge weight is unique has a unique MST. (3 points) (e) Prim's and Kruskal's algorithms will always return the same MST. (3 points)