Let s, t (st) be vertices of a graph G and assume that there is an edge ab such that if we remove ab, then the graph splits into two components, G₁ and G₂ such that G₁ contains s, t and a, while G₂ contains b. (An example of such a graph is shown below.) Show that no path from s to t in G contains any vertex of G2. Assume now that G represents an electrical network where s is the source, t is the sink and the edges have positive resistances. What can you conclude about the currents in the edges of G₂?
Let s, t (st) be vertices of a graph G and assume that there is an edge ab such that if we remove ab, then the graph splits into two components, G₁ and G₂ such that G₁ contains s, t and a, while G₂ contains b. (An example of such a graph is shown below.) Show that no path from s to t in G contains any vertex of G2. Assume now that G represents an electrical network where s is the source, t is the sink and the edges have positive resistances. What can you conclude about the currents in the edges of G₂?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![) Let s, t (s ‡ t) be vertices of a graph G and assume that there is an edge ab such that
if we remove ab, then the graph splits into two components, G₁ and G₂ such that G₁
contains s,
t and a, while G₂ contains b. (An example of such a graph is shown below.)
Show that no path from s to t in G contains any vertex of G₂. Assume now that G
represents an electrical network where s is the source, t is the sink and the edges have
positive resistances. What can you conclude about the currents in the edges of G₂?
G₁
G₂](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba6de5e3-51c1-4a9f-86c0-e5ac1d8a9ad1%2F8eec1d36-2f65-411a-bcb5-77043f8f74c7%2F5uluty_processed.jpeg&w=3840&q=75)
Transcribed Image Text:) Let s, t (s ‡ t) be vertices of a graph G and assume that there is an edge ab such that
if we remove ab, then the graph splits into two components, G₁ and G₂ such that G₁
contains s,
t and a, while G₂ contains b. (An example of such a graph is shown below.)
Show that no path from s to t in G contains any vertex of G₂. Assume now that G
represents an electrical network where s is the source, t is the sink and the edges have
positive resistances. What can you conclude about the currents in the edges of G₂?
G₁
G₂
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