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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
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.]
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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