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22 Consider the folkowing graph ol G a) List the components of the to llowing graphs: GL =G- {c} Ge=G- {d} G3 = G-{i} G4 = G-{e} Gg = G-{he, gf} G6 = G-{di3

22 Consider the folkowing graph ol G a) List the components of the to llowing graphs: GL =G- {c} Ge=G- {d} G3 = G-{i} G4 = G-{e} Gg = G-{he, gf} G6 = G-{di3

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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### Graph Analysis and Component Listing #### Graph Description: The graph is a connected network consisting of multiple vertices and edges. The vertices are labeled as follows: a, b, c, d, e, f, g, h, i, and j. The edges connect these vertices in a specific arrangement: - Vertex "a" is connected to vertices "b" and "c". - There is a triangular connection among vertices "a", "b", and "c". - Vertex "c" connects to "d". - Vertex "d" is connected to vertices "e" and "i". - Vertex "e" connects to "f". - Vertices "f", "g", "h", and "e" form a quadrilateral shape, with an inner loop between "e", "f", "g", and "h". - Vertex "j" forms a loop with itself, connected to vertex "i". ### Question Part (a): **List the components of the following graphs:** - **\(G_1 = G - \{c\}\)**: Graph without vertex "c". - **\(G_2 = G - \{d\}\)**: Graph without vertex "d". - **\(G_3 = G - \{i\}\)**: Graph without vertex "i". - **\(G_4 = G - \{e\}\)**: Graph without vertex "e". - **\(G_5 = G - \{he, gf\}\)**: Graph without edges "he" and "gf". - **\(G_6 = G - \{di\}\)**: Graph without edge "di". The task involves identifying the new components formed when the specified vertices or edges are removed from the original graph \(G\).
Transcribed Image Text:### Graph Analysis and Component Listing #### Graph Description: The graph is a connected network consisting of multiple vertices and edges. The vertices are labeled as follows: a, b, c, d, e, f, g, h, i, and j. The edges connect these vertices in a specific arrangement: - Vertex "a" is connected to vertices "b" and "c". - There is a triangular connection among vertices "a", "b", and "c". - Vertex "c" connects to "d". - Vertex "d" is connected to vertices "e" and "i". - Vertex "e" connects to "f". - Vertices "f", "g", "h", and "e" form a quadrilateral shape, with an inner loop between "e", "f", "g", and "h". - Vertex "j" forms a loop with itself, connected to vertex "i". ### Question Part (a): **List the components of the following graphs:** - **\(G_1 = G - \{c\}\)**: Graph without vertex "c". - **\(G_2 = G - \{d\}\)**: Graph without vertex "d". - **\(G_3 = G - \{i\}\)**: Graph without vertex "i". - **\(G_4 = G - \{e\}\)**: Graph without vertex "e". - **\(G_5 = G - \{he, gf\}\)**: Graph without edges "he" and "gf". - **\(G_6 = G - \{di\}\)**: Graph without edge "di". The task involves identifying the new components formed when the specified vertices or edges are removed from the original graph \(G\).
**Exercise: Identifying Bridges in Graph Theory** **b) What are the bridges of the graph \( G \)?** In this exercise, students are asked to identify the bridges within a given graph \( G \). A *bridge* in graph theory is an edge that, if removed, causes the graph to become disconnected. Identifying bridges is crucial for understanding the structure and vulnerability of networks. Students should carefully examine all edges of the graph \( G \) to determine which are critical for maintaining the graph's connectivity. (Note: As there is no accompanying graph in the image, students should refer to the specific graph provided in their course materials.)
Transcribed Image Text:**Exercise: Identifying Bridges in Graph Theory** **b) What are the bridges of the graph \( G \)?** In this exercise, students are asked to identify the bridges within a given graph \( G \). A *bridge* in graph theory is an edge that, if removed, causes the graph to become disconnected. Identifying bridges is crucial for understanding the structure and vulnerability of networks. Students should carefully examine all edges of the graph \( G \) to determine which are critical for maintaining the graph's connectivity. (Note: As there is no accompanying graph in the image, students should refer to the specific graph provided in their course materials.)
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