I need help from question e, f, and g T(7) Graph Theory and Matrices. A graph G is shown at right.(a) What is the degree of each vertex of the graph?deg(1) = 3deg(2) = 2deg(4)deg(5) = 4If you sum your six answers above, do you notice anything about the sum?16How many edges does the graph have?deg(3) = 3deg(6) = 3(g) What would you expect to be the (3,4) entry of BTB?What about the (3,8)-entry of BTB ? In each case, why?Linear Algebra€4(b) Write down the adjacency matrix A of G.2nd row of A² = [2,2,1,0,1,1] There is I Puth of lengthsfrom 2 to 4 veter(c) What is the meaning of the (2,4)-entry of 4³ ? Support your answer with observations about the graph. Be very specific.(2,4)-entry of A³= 2(0) + 2(0)+ (1) + (0) + (1) (0) + (0) + (0) = / →(d) What is the meaning of the (3,4)-entry of A4? Support your answer with observations about the graph. Be very specific.(e) Write down the vertex-edge incidence matrix B, using the edge labels in the figure. What are the dimensions of matrix B?(f) What would you expect to be the (3,4) entry of BBT?What about the (3,6)-entry of BBT? In each case, why?

Answered: Image /qna-images/answer/de29763f-95d0-4803-a242-895b56d474b9.jpg

(e) Write down the vertex-edge incidence matrix B, using the edge labels in the figure. What are the dimensions of matrix B? (f) What would you expect to be the (3,4) entry of BBT? What about the (3,6)-entry of BBT? In each case, why? (g) What would you expect to be the (3,4) entry of BTB? What about the (3,8)-entry of BTB ? In each case, why?

(e) Write down the vertex-edge incidence matrix B, using the edge labels in the figure. What are the dimensions of matrix B? (f) What would you expect to be the (3,4) entry of BBT? What about the (3,6)-entry of BBT? In each case, why? (g) What would you expect to be the (3,4) entry of BTB? What about the (3,8)-entry of BTB ? In each case, why?

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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Question

I need help from question e, f, and g

T
(7) Graph Theory and Matrices. A graph G is shown at right.
(a) What is the degree of each vertex of the graph?
deg(1) = 3
deg(2) = 2
deg(4)
deg(5) = 4
If you sum your six answers above, do you notice anything about the sum?
16
How many edges does the graph have?
deg(3) = 3
deg(6) = 3
(g) What would you expect to be the (3,4) entry of BTB?
What about the (3,8)-entry of BTB ? In each case, why?
Linear Algebra
€4
(b) Write down the adjacency matrix A of G.
2nd row of A² = [2,2,1,0,1,1] There is I Puth of lengths
from 2 to 4 veter
(c) What is the meaning of the (2,4)-entry of 4³ ? Support your answer with observations about the graph. Be very specific.
(2,4)-entry of A³= 2(0) + 2(0)+ (1) + (0) + (1) (0) + (0) + (0) = / →
(d) What is the meaning of the (3,4)-entry of A4? Support your answer with observations about the graph. Be very specific.
(e) Write down the vertex-edge incidence matrix B, using the edge labels in the figure. What are the dimensions of matrix B?
(f) What would you expect to be the (3,4) entry of BBT?
What about the (3,6)-entry of BBT? In each case, why?

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Step 1: Concept of Incidence matrix

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Step 3: Finding (3,4)th entry of $BB^T$

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