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
Related questions
Question
Transcribed Image Text: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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