The exercise is as followed: "Let H be the smallest class that contains the graphs K′5 and K′3,3, and is closed under isomorphism and 2-sum. Prove that every graph in H is planar."

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The exercise is as followed: "Let H be the smallest class that contains the graphs K′5 and K′3,3, and is closed under isomorphism and 2-sum. Prove that every graph in H is planar."

I think I know how to do the 2-sum of K'5 and K'3,3 (as you can find attached) but I don't know whether it's correct and what I got to do now? Thank you very much for the help!!

Ex. 3:
મ
Ne
^^
GO₂ H
a)
d(v)
G₁
G₂
le
G₁ Q₂H₁
G₁zH₁
2 degree?
2
Vertices
Gu₂ ltz
13
no degree
Svertex
e
K313
На
H₂
1
G₂₂ H₁
3
2 degree 5
√vertex
G₂ E2 H₂
idegree
2
vertex
Transcribed Image Text:Ex. 3: મ Ne ^^ GO₂ H a) d(v) G₁ G₂ le G₁ Q₂H₁ G₁zH₁ 2 degree? 2 Vertices Gu₂ ltz 13 no degree Svertex e K313 На H₂ 1 G₂₂ H₁ 3 2 degree 5 √vertex G₂ E2 H₂ idegree 2 vertex
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