Explanation Given info: Calculation: Kruskal’s algorithm: Start from a graph T that contains only the vertices and no edges. Repeatedly select the edge in the graph G with the smallest weight (that doesn’t cause a circuit) and add it to the graph T. Once the graph is connected. We have found a minimum spanning tree. We ignore all edges that were previously added to the graph. First iteration: The edge with the smallest weight is the edge between u and x with weight 1, thus we add the edge [ u , x ] to the minimum spanning tree. Added edge = [ u , x ] Second iteration: the edges with the smallest weight are the edges between x and y and the edge between u and v with weight 2 each. 2 will choose to add the edge [ u , v ] first to the minimum spanning tree. Note: You could also choose to use the edge [ x , y ] first. Added edge = [ u , v ] Third iteration: The edge with the smallest weight is the edge between x and y with weight 2, thus we add the edge [ a , e ] to the minimum spanning tree. Added edge = [ x , y ] Forth iteration: The edge with the smallest weight is the edge between t and w with weight 3, thus we add edge [ t , w ] to the minimum spanning tree. Added edge = [ t , w ] Fifth iteration: The edges with the smallest weight are the edge between w and x and the edge between y and z with weight 5 each. I will choose to add the edge [ w , x ] to the minimum spanning tree. Note: You could also choose to use the edge [ c , e ] instead. Added edge = [ w , x ] Sixth iteration: The edge with the smallest weight is the edge between y and z with weight 5, thus we add the edge [ y , z ] to the minimum spanning tree To determine (b) Find all minimum spanning trees that can be obtained using Prim’s algorithm starting with vertex a or t. indicate the order in which edges are added to form each tree.

5th Edition

ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 10.6, Problem 10ES

To determine

(a)

For the graph, find all minimum spanning trees that can be obtained using

Kruskal’s algorithm. Indicate the order in which edges are added to form each tree.

To determine

(b)

Find all minimum spanning trees that can be obtained using Prim’s algorithm starting with vertex a or t. indicate the order in which edges are added to form each tree.

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Chapter 10 Solutions

Discrete Mathematics With Applications

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(a) For the graph, find all minimum spanning trees that can be obtained using Kruskal’s algorithm. Indicate the order in which edges are added to form each tree.

Solution Summary: The author explains Kruskal's algorithm for finding minimum spanning trees.

(a) For the graph, find all minimum spanning trees that can be obtained using Kruskal’s algorithm. Indicate the order in which edges are added to form each tree.

(b) Find all minimum spanning trees that can be obtained using Prim’s algorithm starting with vertex a or t. indicate the order in which edges are added to form each tree.

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Chapter 10 Solutions

(a)

For the graph, find all minimum spanning trees that can be obtained using

Kruskal’s algorithm. Indicate the order in which edges are added to form each tree.

(b)

Find all minimum spanning trees that can be obtained using Prim’s algorithm starting with vertex a or t. indicate the order in which edges are added to form each tree.