Let G be the graph on vertices V1, V2, ..., U8 with the following adjacency matrix:0100 0001 0 1 000010100 100 100000110001000000 0 0 1 0000000 100001 1 100 000Sketch all the graphs (up to isomorphism) on four vertices that are isomorphicto an induced subgraph of G (identifying a suitable induced subgraph in eachcase).Sketch all the graphs (up to isomorphism) on four vertices that are not iso-morphic to an induced subgraph of G.Find a graph on four vertices that is isomorphic to a subgraph, but not to aninduced subgraph, of G. Explain your answer.

soluyion:The given adjacency matrix is as follows: 0 1 0 0 0 0 0 11 0 1 0 0 0 0 10 1 0 1 0 0 0 00 0…

Answered: Let G be the graph on vertices V1, V2,…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 69EQ

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Question

Let G be the graph on vertices V1, V2, ..., U8 with the following adjacency matrix:
0100 000
1 0 1 00001
0
100 100 1
000001
10
00100000
0 0 0 1 0000
000 10000
1 1 100 000
Sketch all the graphs (up to isomorphism) on four vertices that are isomorphic
to an induced subgraph of G (identifying a suitable induced subgraph in each
case).
Sketch all the graphs (up to isomorphism) on four vertices that are not iso-
morphic to an induced subgraph of G.
Find a graph on four vertices that is isomorphic to a subgraph, but not to an
induced subgraph, of G. Explain your answer.

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