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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(ce) = 14, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (b) Show that the minimum spanning tree found by Kruskal's algorithms is in fact the unique minimum spanning tree of (G, w).

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(ce) = 14, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (b) Show that the minimum spanning tree found by Kruskal's algorithms is in fact the unique minimum spanning tree of (G, w).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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1. Consider the network (G, w) with V(G) = {a, b, c, d, e, ƒ}, 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(ce) = 14, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (b) Show that the minimum spanning tree found by Kruskal's algorithms is in fact the unique minimum spanning tree of (G, w).
Transcribed Image Text:1. Consider the network (G, w) with V(G) = {a, b, c, d, e, ƒ}, 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(ce) = 14, w(bd) = 6, w(be) = 13, w(bf) = 10, w(cd) = 4, w(cf) = 2, w(de) = 16, w(df) = 11, w(ef) = 7. (b) Show that the minimum spanning tree found by Kruskal's algorithms is in fact the unique minimum spanning tree of (G, w).
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