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Suppose G is an undirected graph with vertices a, b, c, d, e, f with the adjacency matrix given below

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Suppose G is an undirected graph with vertices a, b, c, d, e, f with the adjacency matrix given below. (where alphabetical order is used to determine the rows and columns of the adjacency matrix). Find

[ 0 1 0 1 0 0

1 0 0 1 1 1 

0 0 0 0 1 1

1 1 0 0 1 0

0 1 1 1 0 1

0 1 1 0 1 0]

Find;

a) The number of vertices in G.

b) The number of edges in G.

c) The degree of vertex e.

d) The number of loops.

e) The length of the longest simple path in G.

f) Determine if G has an Euler path. Give your reason.