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3. Consider a network (G, w). Let c € R, and let m: E(G) → R such that m(e) = w(e) + c for all e € E(G). (a) Show that T is a minimum spanning tree of (G, w) if and only if it is a minimum spanning tree of (G,m).

3. Consider a network (G, w). Let c € R, and let m: E(G) → R such that m(e) = w(e) + c for all e € E(G). (a) Show that T is a minimum spanning tree of (G, w) if and only if it is a minimum spanning tree of (G,m).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 74EQ
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3. Consider a network (G, w). Let c ER, and let m: E(G) → R such that m(e) = w(e) + c for all e Є E(G). (a) Show that T is a minimum spanning tree of (G, w) if and only if it is a minimum spanning tree of (G,m).
Transcribed Image Text:3. Consider a network (G, w). Let c ER, and let m: E(G) → R such that m(e) = w(e) + c for all e Є E(G). (a) Show that T is a minimum spanning tree of (G, w) if and only if it is a minimum spanning tree of (G,m).
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