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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
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
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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