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Problem 2. Consider the following two graphs: G₁ V₁=(a,b,c,d,e,f,g) E₁={{a,b),(a,d},{b,c}),(b,d},{b,e},{b,f},{c,g},{d,e},{e,f},{f,g}}. G₂ V2=(V1, V2, V3, V4, VS, V6, V7), E2={{V1,V4},{V1,VS),{V1,V7), (v2,v3), (V2,V6},{V3,VS), (Va,V7},{V4,VS),(VS,VG),(VS,V7}} Let f: V₁ V₂ be a function that takes the vertices of Graph 1 to vertices of Graph 2. The function is given by the following table: X d f f(x) V4 V6 V₂ V3 a. Does f define an isomorphism between Graph 1 and Graph 2? Justify your answer. b. Define a new function g (with gef) that defines an isomorphism between Graph 1 and Graph 2. c. Is the graph pictured below isomorphic to Graph 1 and Graph 2? Explain. a a b Vs d с V₁ b G V7
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Transcribed Image Text:Problem 2. Consider the following two graphs: G₁ V₁=(a,b,c,d,e,f,g) E₁={{a,b),(a,d},{b,c}),(b,d},{b,e},{b,f},{c,g},{d,e},{e,f},{f,g}}. G₂ V2=(V1, V2, V3, V4, VS, V6, V7), E2={{V1,V4},{V1,VS),{V1,V7), (v2,v3), (V2,V6},{V3,VS), (Va,V7},{V4,VS),(VS,VG),(VS,V7}} Let f: V₁ V₂ be a function that takes the vertices of Graph 1 to vertices of Graph 2. The function is given by the following table: X d f f(x) V4 V6 V₂ V3 a. Does f define an isomorphism between Graph 1 and Graph 2? Justify your answer. b. Define a new function g (with gef) that defines an isomorphism between Graph 1 and Graph 2. c. Is the graph pictured below isomorphic to Graph 1 and Graph 2? Explain. a a b Vs d с V₁ b G V7
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