Graph Theory: Consider the following incidence matrix of a graph G=(V,E) with V={a,b,c,d} and {e_(1),e_(2),e_(3),e_(1),e_(5),e_(6)} 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 solutionspile.com

Question

Graph Theory: Consider the following incidence matrix of a graph

G=(V,E)

with

V={a,b,c,d}

and

{e_(1),e_(2),e_(3),e_(1),e_(5),e_(6)}

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(A^(2))

? [The question is not about the value.] (f) Without direct calculations, find one of the eigenvalues of

A

based on the information you can get from

A

. Then calculate its corresponding eigenvector.

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