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Consider the network (G, w) with V(G) = {a, b, c, d, e, f}, E(G)= {ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef}, and w(ab) = 9, w(ac) = 8, w(ad) = 12, w(ae) = 3, w(af) = 15, w(bc) = 5, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(ce) = 14, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (a) Use Kruskal's algorithm to find a minimum spanning tree of (G, w). List the edges of the tree in the order in which they are added, and draw the tree.

Consider the network (G, w) with V(G) = {a, b, c, d, e, f}, E(G)= {ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef}, and w(ab) = 9, w(ac) = 8, w(ad) = 12, w(ae) = 3, w(af) = 15, w(bc) = 5, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(ce) = 14, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (a) Use Kruskal's algorithm to find a minimum spanning tree of (G, w). List the edges of the tree in the order in which they are added, and draw the tree.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 4P
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1. Consider the network (G, w) with V(G)= {a, b, c, d, e, f}, E(G)= {ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef}, and w(ab) = 9, w(ac) = 8, w(ad) = 12, w(ae) = 3, w(af) = 15, w(bc) = 5, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(ce) = 14, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (a) Use Kruskal's algorithm to find a minimum spanning tree of (G, w). List the edges of the tree in the order in which they are added, and draw the tree.
Transcribed Image Text:1. Consider the network (G, w) with V(G)= {a, b, c, d, e, f}, E(G)= {ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef}, and w(ab) = 9, w(ac) = 8, w(ad) = 12, w(ae) = 3, w(af) = 15, w(bc) = 5, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(ce) = 14, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (a) Use Kruskal's algorithm to find a minimum spanning tree of (G, w). List the edges of the tree in the order in which they are added, and draw the tree.
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