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ट AA a. determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why. D. If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why. 5. A Be C D E

ट AA a. determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why. D. If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why. 5. A Be C D E

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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Certainly! Here's the transcription and explanation for an educational website: --- **Graph Theory Exercise** **Problem 15:** a. Determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why. b. If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why. **Graph Description:** The graph is a complete bipartite graph K3,2, consisting of five vertices labeled A, B, C, D, and E. - There are edges connecting each vertex in the set {A, B, C} to each vertex in the set {D, E}. - The edges are: AD, AE, BD, BE, CD, and CE. **Graph Analysis:** - **Vertices A, B, C:** Each has a degree of 2. - **Vertices D, E:** Each has a degree of 3. **Eulerian Graph Criteria:** - A graph is Eulerian if it is connected and each vertex has an even degree. - A graph has an Euler path if it is connected and exactly two vertices have an odd degree. **Conclusion:** - Since vertices D and E have an odd degree, the graph is not Eulerian. - However, the graph does have an Euler path because exactly two vertices (D and E) have an odd degree. An example Euler path is: A - D - B - E - C.
Transcribed Image Text:Certainly! Here's the transcription and explanation for an educational website: --- **Graph Theory Exercise** **Problem 15:** a. Determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why. b. If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why. **Graph Description:** The graph is a complete bipartite graph K3,2, consisting of five vertices labeled A, B, C, D, and E. - There are edges connecting each vertex in the set {A, B, C} to each vertex in the set {D, E}. - The edges are: AD, AE, BD, BE, CD, and CE. **Graph Analysis:** - **Vertices A, B, C:** Each has a degree of 2. - **Vertices D, E:** Each has a degree of 3. **Eulerian Graph Criteria:** - A graph is Eulerian if it is connected and each vertex has an even degree. - A graph has an Euler path if it is connected and exactly two vertices have an odd degree. **Conclusion:** - Since vertices D and E have an odd degree, the graph is not Eulerian. - However, the graph does have an Euler path because exactly two vertices (D and E) have an odd degree. An example Euler path is: A - D - B - E - C.
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