2. Say that for any pair of people, they either both know each other, or they arestrangers (neither knows each other). Prove that in any party of six people, there isa group of three that either all know each other, or all are strangers.(Hint: how can you model this problem using a graph?)

Answered: Image /qna-images/answer/bdcb9d69-fdfd-45ee-ad9b-7472e108920b.jpg

Answered: 2. Say that for any pair of people,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3. Consider the following graphs G₁, G2, and G3 G₁ is the graph with vertex set {1, 2, 3, 4, X5, X6, 7, 8}, and edge set {1x2, X1X7, X1X8, X2X3, X3X4, X3 X5, X3X6, X3X7, X4X5, X5X6, X7X8}. • G₂ is the graph with vertex set (y₁, Y2, Y3, Y4, Y5, Y6, y7, ys} and adjacency matrix: Y1 Y2 Y3 Y4 Y5 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 000 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 27 28 Y6 Y7 Y8 • G3 is the graph with vertex set {21, 22, 23, 24, 25, 26, 27, 28} and incidence matrix: 2₁ 1 1 22 23 24 25 26 1 0 0000 0 00 0 0 1 0 0 000 00 0 1 0 1 1 0000 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 00000000011 (a) Exactly two of the three graphs are ismorphic. Which two are they? (b) Provide an isomorphism between the two graphs you picked in part (a).
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2. Say that for any pair of people, they either both know each other, or they are strangers (neither knows each other). Prove that in any party of six people, there is a group of three that either all know each other, or all are strangers. (Hint: how can you model this problem using a graph?)