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Consider the given graphs: 11₂ Ug 17 1₂ 116 115 113 14 V8 V₁ V6 1/₂ V5 V₁ G H Click and drag the statements in correct order either to show that these graphs are not isomorphic or to find an isomorphism between them using paths.

Consider the given graphs: 11₂ Ug 17 1₂ 116 115 113 14 V8 V₁ V6 1/₂ V5 V₁ G H Click and drag the statements in correct order either to show that these graphs are not isomorphic or to find an isomorphism between them using paths.

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 given graphs: Ug U₂ 16 Us U₂ Us Vs V7 V₁ V6 V₂ V₂ V₂ G H Click and drag the statements in correct order either to show that these graphs are not isomorphic or to find an isomorphism between them using paths. Having thus been led to the only possible isomorphism, check that the 12 edges of G do not correspond to the 12 edges of H; hence the two graphs are not isomorphic. So try to construct an isomorphism that matches them, say u₁ → V₂ and us → V6. Proceeding along similar lines, complete the bijection with us Va, UgV7, and U> → Vs. Now u, is adjacent to uz and us, and v₂ is adjacent to vi and v), so u₂v and us V3 Since us is the other vertex adjacent to us and v4 is the other vertex adjacent to V3, U4 V4. Having thus been led to the only possible isomorphism, check that the 12 edges of G exactly correspond to the 12 edges of H, and the two graphs are isomorphic.
Transcribed Image Text:Consider the given graphs: Ug U₂ 16 Us U₂ Us Vs V7 V₁ V6 V₂ V₂ V₂ G H Click and drag the statements in correct order either to show that these graphs are not isomorphic or to find an isomorphism between them using paths. Having thus been led to the only possible isomorphism, check that the 12 edges of G do not correspond to the 12 edges of H; hence the two graphs are not isomorphic. So try to construct an isomorphism that matches them, say u₁ → V₂ and us → V6. Proceeding along similar lines, complete the bijection with us Va, UgV7, and U> → Vs. Now u, is adjacent to uz and us, and v₂ is adjacent to vi and v), so u₂v and us V3 Since us is the other vertex adjacent to us and v4 is the other vertex adjacent to V3, U4 V4. Having thus been led to the only possible isomorphism, check that the 12 edges of G exactly correspond to the 12 edges of H, and the two graphs are isomorphic.
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