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O For the Pollowing graphs, list r(G), ECG), and the values of the incidence mapping P6 : e, a) ei en eu 4 es' 3 c) eg d) 1 e, e3 3 3 4 eu -er

O For the Pollowing graphs, list r(G), ECG), and the values of the incidence mapping P6 : e, a) ei en eu 4 es' 3 c) eg d) 1 e, e3 3 3 4 eu -er

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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1. For the following graphs, list V(G), E(G), and the values of the incidence mapping ψG: a) - **Graph**: A triangle formed by vertices 1, 2, and 3. Edges e₁ connects vertices 1 and 2, e₂ connects vertices 2 and 3, and e₃ is a loop on vertex 3. - **Vertices V(G)**: {1, 2, 3} - **Edges E(G)**: {e₁, e₂, e₃} - **Incidence Mapping ψG**: - e₁: (1, 2) - e₂: (2, 3) - e₃: (3, 3) b) - **Graph**: A rectangle with vertices 1, 2, 3, and 4. Diagonal edge e₄ connects vertices 1 and 3. Loop e₃ at vertex 2. - **Vertices V(G)**: {1, 2, 3, 4} - **Edges E(G)**: {e₁, e₂, e₃, e₄, e₅, e₆} - **Incidence Mapping ψG**: - e₁: (1, 2) - e₂: (2, 3) - e₃: (2, 2) - e₄: (1, 3) - e₅: (3, 4) - e₆: (4, 1) c) - **Graph**: A path from vertex 1 to vertex 4 with a loop e₂ at vertex 2. - **Vertices V(G)**: {1, 2, 3, 4} - **Edges E(G)**: {e₁, e₂, e₃, e₄} - **Incidence Mapping ψG**: - e₁: (1, 2) - e₂: (2, 2) - e₃: (2, 3) - e₄: (1, 4) d) - **Graph**: A P-shape with vertices 1, 2, and 3. A loop e₂ at vertex 3. - **Vertices
Transcribed Image Text:1. For the following graphs, list V(G), E(G), and the values of the incidence mapping ψG: a) - **Graph**: A triangle formed by vertices 1, 2, and 3. Edges e₁ connects vertices 1 and 2, e₂ connects vertices 2 and 3, and e₃ is a loop on vertex 3. - **Vertices V(G)**: {1, 2, 3} - **Edges E(G)**: {e₁, e₂, e₃} - **Incidence Mapping ψG**: - e₁: (1, 2) - e₂: (2, 3) - e₃: (3, 3) b) - **Graph**: A rectangle with vertices 1, 2, 3, and 4. Diagonal edge e₄ connects vertices 1 and 3. Loop e₃ at vertex 2. - **Vertices V(G)**: {1, 2, 3, 4} - **Edges E(G)**: {e₁, e₂, e₃, e₄, e₅, e₆} - **Incidence Mapping ψG**: - e₁: (1, 2) - e₂: (2, 3) - e₃: (2, 2) - e₄: (1, 3) - e₅: (3, 4) - e₆: (4, 1) c) - **Graph**: A path from vertex 1 to vertex 4 with a loop e₂ at vertex 2. - **Vertices V(G)**: {1, 2, 3, 4} - **Edges E(G)**: {e₁, e₂, e₃, e₄} - **Incidence Mapping ψG**: - e₁: (1, 2) - e₂: (2, 2) - e₃: (2, 3) - e₄: (1, 4) d) - **Graph**: A P-shape with vertices 1, 2, and 3. A loop e₂ at vertex 3. - **Vertices
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