Consider the undirected graph below:

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Using Prim's algorithm to construct a minimum spanning tree starting with node a, which one of the following sequences of edges represents a possible order in which the edges would be added to construct the minimum spanning tree?

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UGC NET Computer Science (Paper 2) 2020 Official Paper
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  1. (a, b), (b, h), (g, h), (f, g), (c, f), (c, i), (c, d), (d, e) 
  2. (a, b), (b, h), (g, h), (g, i), (c, i), (c, f), (c, d), (d, e) 
  3. (a, b), (b, c), (c, i), (c, f), (f, g), (g, h), (c, d), (d, e) 
  4. (a, b), (g, h), (g, f), (c, f), (c, i), (f, e), (b, c), (d, e) 

Answer (Detailed Solution Below)

Option 3 : (a, b), (b, c), (c, i), (c, f), (f, g), (g, h), (c, d), (d, e) 
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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The correct answer is option 1 and option 3.

Concept:

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges(V – 1 ) of a connected, edge-weighted undirected graph G(V, E) that connects all the vertices together, without any cycles and with the minimum possible total edge weight.

Key Points

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The final sequence will be (a, b), (b, c), (c, i), (c, f), (f, g), (g, h), (c, d), (d, e) with a cost 37.  

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Another final sequence is (a, b), (a, h), (g, h), (f, g), (c, f), (c, i), (c, d), (d, e) with a cost is 37(Two sequences possible ).

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