3. Consider the following graphs G₁, G2, and G3G₁ 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:Y1Y2Y3Y4Y50 1 0 1 1 1 1 010 1 00 0 0 001 0000 1 11 0 0 010001 0 0 1 0 1 0 01 0 01 0 10 10 0 00 0 0 0 10 0 1 0 0 0 1 02728Y6Y7Y8• G3 is the graph with vertex set {21, 22, 23, 24, 25, 26, 27, 28} and incidence matrix:2₁ 1 122232425261 0 0000 0 000 0 10 0 000 0001 011000000 0 0011 1 0 0 0 00 0 0 0 01 0 1 0 0 001 11 1 01 0 0 00 0 0 0 0 0 0 0 1 0 100000000011(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).

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 {x1x2, X1X7, X1X8, X2X3, X3 X4, X3X5, X3X6, X3X7, X4 X5, X5 X6, X7X8}. • G₂ is the graph with vertex set (y₁, Y2, Y3, Y4, Y5, Y6, y7, ys} and adjacency matrix: 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 000 1 0 0 1 0 1 0 0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 • G3 is the graph with vertex set {21, 22, 23, 24, 25, 26, 27, 28} and incidence matrix: 1 1 0 0 1 0 0 0 0 0 27 28 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 2₁ 1 1 22 23 24 25 26 1 0 0000 0 00 00 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0000 0 1 1 0 0 0 0 1 0 1 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).

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 {x1x2, X1X7, X1X8, X2X3, X3 X4, X3X5, X3X6, X3X7, X4 X5, X5 X6, X7X8}. • G₂ is the graph with vertex set (y₁, Y2, Y3, Y4, Y5, Y6, y7, ys} and adjacency matrix: 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 000 1 0 0 1 0 1 0 0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 • G3 is the graph with vertex set {21, 22, 23, 24, 25, 26, 27, 28} and incidence matrix: 1 1 0 0 1 0 0 0 0 0 27 28 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 2₁ 1 1 22 23 24 25 26 1 0 0000 0 00 00 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0000 0 1 1 0 0 0 0 1 0 1 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).

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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