Tutorial Activity 8

# Tutorial Activity 8

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MH 8300 Tutorial Activity 8 Minimum Spanning Tree Group Members Name NTU Email ID Marks : /2

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MH 8300 Tutorial Activity 8 Minimum Spanning Tree Consider the following undirected edge-weighted graph G on the vertex set V = {A, B, C, D, E, F, G, H, I, J}. Question 1. Answer the following questions. (a) Apply Kruskal’s algorithm to find T , the minimum spanning tree of G . (Trace the dotted lines to show the MST.) (b) Determine the weight of the minimum spanning tree T .
Definition. (Induced Subgraph) Let G be a graph with vertex set V . Suppose V 0 is a subset of V . A graph G [ V 0 ] is an induced subgraph of G by V 0 which is obtained by deleting all vertices in V \ V 0 and all edges incident to them from graph G . Question 2. Consider the vertex set V 1 = {D, E, F, G, H, I, J} which is a subset of V . (a) Draw G 1 , the induced subgraph of G by V 1 . (b) Apply Kruskal’s algorithm to find T 1 , the minimum spanning tree of G 1 . (c) Determine the weight of the minimum spanning tree T 1 . (d) Draw the induced subgraph of T by V 1 . (Note : T is the MST found in Qn 1(a))

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