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,V),(v2,v3), (V2,V6), (V3,VS), (Va,V7},{V4,Vs),(vs,V6},{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
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,V),(v2,v3), (V2,V6), (V3,VS), (Va,V7},{V4,Vs),(vs,V6},{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
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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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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