Graph Theory: Consider the following incidence matrix of a graph G = (V, E) with V = {a,b,c,d) and {e₁,e2, €3, e4, e5, e6} M = e1 1 -1 C 0 d 0 0 a €3 e4 e5 €6 -1 0 1 -1 0 -1 0 0 0 0 0 1 1 1 -1 0 -1 b 81100 €2 Based on the information you obtain from the incidence matrix M, answer these questions: (a) What type of graph does M represent? (b) Find the adjacency matrix A for this graph. (c) Draw the graph. (d) How many paths of length 2 are there between nodes b and c (without direct counting)? (e) In terms of connectivity of the graph, what is your interpretation of tr(A²)? [The question is not about the value.]
Graph Theory: Consider the following incidence matrix of a graph G = (V, E) with V = {a,b,c,d) and {e₁,e2, €3, e4, e5, e6} M = e1 1 -1 C 0 d 0 0 a €3 e4 e5 €6 -1 0 1 -1 0 -1 0 0 0 0 0 1 1 1 -1 0 -1 b 81100 €2 Based on the information you obtain from the incidence matrix M, answer these questions: (a) What type of graph does M represent? (b) Find the adjacency matrix A for this graph. (c) Draw the graph. (d) How many paths of length 2 are there between nodes b and c (without direct counting)? (e) In terms of connectivity of the graph, what is your interpretation of tr(A²)? [The question is not about the value.]
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 1) Graph Theory: Consider the following incidence matrix of a graph G = (V, E) with V
{a,b,c,d) and {e₁,e2, e3, e4, e5, e6}
M =
1
-1
с
0
d 0
a
b
e2
-1
1
0
0
€3 e4
0 1
-1 0
0 0
1 -1
e5 e6
-1
0
0 0
1
1
0 −1
Based on the information you obtain from the incidence matrix M, answer these questions:
(a) What type of graph does M represent?
(b) Find the adjacency matrix A for this graph.
(c) Draw the graph.
(d) How many paths of length 2 are there between nodes b and c (without direct counting)?
(e) In terms of connectivity of the graph, what is your interpretation of tr(A²)? [The question
is not about the value.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F305a57b9-91a1-45b1-a922-55d845f786ad%2Fd0d7b8d2-1667-4d0b-b4ab-ac93aeb0e1bb%2Fkwpxz_processed.png&w=3840&q=75)
Transcribed Image Text:Question 1) Graph Theory: Consider the following incidence matrix of a graph G = (V, E) with V
{a,b,c,d) and {e₁,e2, e3, e4, e5, e6}
M =
1
-1
с
0
d 0
a
b
e2
-1
1
0
0
€3 e4
0 1
-1 0
0 0
1 -1
e5 e6
-1
0
0 0
1
1
0 −1
Based on the information you obtain from the incidence matrix M, answer these questions:
(a) What type of graph does M represent?
(b) Find the adjacency matrix A for this graph.
(c) Draw the graph.
(d) How many paths of length 2 are there between nodes b and c (without direct counting)?
(e) In terms of connectivity of the graph, what is your interpretation of tr(A²)? [The question
is not about the value.]
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