Let H be a graph with the following adjacency matrix: 0 1 1 1] 0 1 1001 [1 1 1 0] A = (a) Draw H. Is H a tree? Justify your answer. (b) Compute A². What is the meaning of the number in the first row and first column of A²? (c) Could the matrix A² be the adjacency matrix of a simple graph? If so, draw the graph. If not, explain why.

Let H be a graph with the following adjacency matrix: 0 1 1 1] 0 1 1001 [1 1 1 0] A = (a) Draw H. Is H a tree? Justify your answer. (b) Compute A². What is the meaning of the number in the first row and first column of A²? (c) Could the matrix A² be the adjacency matrix of a simple graph? If so, draw the graph. If not, explain why.

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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