Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 538 — #546
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Chapter 13
Planar Graphs
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Problems for Section 13.8
Exam Problems
Problem 13.2.
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(a) Describe an isomorphism between graphs G 1 and G 2 , and another isomorphism
between G 2 and G 3 .
(b) Why does part .a/ imply that there is an isomorphism between graphs G 1 and
G 3 ?
Let G and H be planar graphs. An embedding E G of G is isomorphic to an embedding
E H of H iff there is an isomorphism from G to H that also maps each
face of E G to a face of E H .
(c) One of the embeddings pictured above is not isomorphic to either of the others.
Which one? Briefly explain why.
(d) Explain why all embeddings of two isomorphic planar graphs must have the