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Consider the two following graphs and answer the following questions. a) Are G and H isomorphic? Why? b) Show that H is bipartite. c) Show that k(G) = 2. d) Show that 2(H) = 2. %3D U5 %3D e) Does G contain any Eulerian circuit? Why? f) Find a Hamiltonian path in H. g) Consider H as a planar representation of a planar Ug U4 graph. Label regions in H, and find degree of each

Consider the two following graphs and answer the following questions. a) Are G and H isomorphic? Why? b) Show that H is bipartite. c) Show that k(G) = 2. d) Show that 2(H) = 2. %3D U5 %3D e) Does G contain any Eulerian circuit? Why? f) Find a Hamiltonian path in H. g) Consider H as a planar representation of a planar Ug U4 graph. Label regions in H, and find degree of each

Advanced Engineering Mathematics
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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Consider the two following graphs and answer the following questions. a) Are G and H isomorphic? Why? b) Show that H is bipartite. c) Show that K(G) = 2. d) Show that 1(H) = 2. e) Does G contain any Eulerian circuit? Why? Find a Hamiltonian path in H. U2 V1 V2 U5 U6 V5 V6 Ug U7 V8 V7 f) g) Consider H as a planar representation of a planar graph. Label regions in H, and find degree of each U4 Uz V4 V3 G H region in H. 2.
Transcribed Image Text:Consider the two following graphs and answer the following questions. a) Are G and H isomorphic? Why? b) Show that H is bipartite. c) Show that K(G) = 2. d) Show that 1(H) = 2. e) Does G contain any Eulerian circuit? Why? Find a Hamiltonian path in H. U2 V1 V2 U5 U6 V5 V6 Ug U7 V8 V7 f) g) Consider H as a planar representation of a planar graph. Label regions in H, and find degree of each U4 Uz V4 V3 G H region in H. 2.
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