13. Given that the matrix 1 0 1 0 1 ГО 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0] 1 1 A = 1 is the adjacency matrix for the graph F, without drawing F, answer the following and justify your answers. You may not use a drawing of F to justify your answers. You may only use properties of the adjacency matrix A.: (a) Is F connected? (b) How many edges are in the graph F? Hint: What does the sum of the entries of A tell you about F? (c) How many paths of length 2 are there from vị to vz in F? Hint: You only need to calculate one entry of a matrix.
13. Given that the matrix 1 0 1 0 1 ГО 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0] 1 1 A = 1 is the adjacency matrix for the graph F, without drawing F, answer the following and justify your answers. You may not use a drawing of F to justify your answers. You may only use properties of the adjacency matrix A.: (a) Is F connected? (b) How many edges are in the graph F? Hint: What does the sum of the entries of A tell you about F? (c) How many paths of length 2 are there from vị to vz in F? Hint: You only need to calculate one entry of a matrix.
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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Transcribed Image Text:13.
Given that the matrix
[o 1 1 1 0 17
1 0 1 1 0 1
1 1 0 0 0 1
1 1 0 0 0 0
0 0 0 0 0 0
[1 1 1 0 0 0
A =
is the adjacency matrix for the graph F, without drawing F, answer the following and justify
your answers. You may not use a drawing of F to justify your answers. You may only
use properties of the adjacency matrix A.:
(a) Is F connected?
(b) How many edges are in the graph F? Hint: What does the sum of the entries of A tell you about
F?
(c) How many paths of length 2 are there from vị to vz in F? Hint: You only need to calculate one
entry of a matrix.
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