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Consider four graphs G1, G2, G3, and G4 pictured in Figure 1. Determine which among the four graphs are isomorphic. 1. For each pair of isomorphic graphs, explicitly write an isomorphism between them. Don't forget to verify that your mapping is an isomorphism. 2. For each pair of graphs that are not isomorphic, give a property that is preserved under isomorphism such that one graph has the property, but the other does not.

Consider four graphs G1, G2, G3, and G4 pictured in Figure 1. Determine which among the four graphs are isomorphic. 1. For each pair of isomorphic graphs, explicitly write an isomorphism between them. Don't forget to verify that your mapping is an isomorphism. 2. For each pair of graphs that are not isomorphic, give a property that is preserved under isomorphism such that one graph has the property, but the other does not.

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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This is a discrete math problem. Please explain each step in detail and do not copy solutions from Chegg. 

Consider four graphs G1, G2, G3, and G4 pictured in Figure 1. Determine which among the four graphs are isomorphic. 1. For each pair of isomorphic graphs, explicitly write an isomorphism between them. Don't forget to verify that your mapping is an isomorphism. 2. For each pair of graphs that are not isomorphic, give a property that is preserved under isomorphism such that one graph has the property, but the other does not.
Transcribed Image Text:Consider four graphs G1, G2, G3, and G4 pictured in Figure 1. Determine which among the four graphs are isomorphic. 1. For each pair of isomorphic graphs, explicitly write an isomorphism between them. Don't forget to verify that your mapping is an isomorphism. 2. For each pair of graphs that are not isomorphic, give a property that is preserved under isomorphism such that one graph has the property, but the other does not.
9. 5. 1 .2 8 10. 7 10 8, 4 3 4 3 (a) G1 (b) G2 1 1 9. 5. 7 8. 3 10 10 8, 7' 24 4 3 6. 5 (d) G4 (c) G3 Figure 1. 4 potentially isomorphic graphs. 2. 6)
Transcribed Image Text:9. 5. 1 .2 8 10. 7 10 8, 4 3 4 3 (a) G1 (b) G2 1 1 9. 5. 7 8. 3 10 10 8, 7' 24 4 3 6. 5 (d) G4 (c) G3 Figure 1. 4 potentially isomorphic graphs. 2. 6)
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