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 fourgraphs are isomorphic.1. For each pair of isomorphic graphs, explicitly write an isomorphism between them. Don'tforget to verify that your mapping is an isomorphism.2. For each pair of graphs that are not isomorphic, give a property that is preserved underisomorphism such that one graph has the property, but the other does not. 9.5.1.2810.7108,4343(a) G1(b) G2119.5.78.310108,7'24436.5(d) G4(c) G3Figure 1. 4 potentially isomorphic graphs.2.6)

Name: This is a discrete math problem. Please explain each step in detail an
Uploaded: 2024-03-20T06:38:44.000Z
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Description: 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 fourgraphs are isomorphic.1. For each pair of isomorphic

The graphs G1 and G4 are isomorphic to each other. Define a mapping F: G1-> G2 by F(1)= 1 , F(4)= 8, F(7)=4 F(2)= 2, F(5)= 9, F(8)= 5 F(3)= 3, F(6)= 10, F(9)= 6 F(10)= 7You can easily check that, F is an isomorphism Alternatively, if you cannot understand that you can alternatively say that G1 and G4 are isomorphic- You can draw G4 as Now see that G1 and G4 are isomorphic to each other 2. a) G1 and G2 are not isomorphic, because G2 contains a 4 cycle (1-6-9-5-1) but G1 has no 4 cycle. b) G1 and G3 are not isomorphic, because G3 contains a 3 cycle (6-8-10-6) but G1 has no 3 cycle. c) G2 and G3 are not isomorphic, because G3 contains a 3 cycle (6-8-10-6) but G2 has no 3 cycle.d) G2 and G4 are not isomorphic, because G2 contains a 4 cycle but G4 has no 4 cycle. e) G3 and G4 are not isomorphic, because G3 contains a 3 cycle but G4 has no 3 cycle. If you have any doubt, ask me. Thank you