Question

Which of the following networks are traversable? Give reasons.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Answer 1

(i)

Node	A	B	C
Order of node	3	6	3

Number of odd nodes = 2

Number of even nodes = 1

Since the figure has only 2 odd nodes, it satisfies the condition of traversability.

Thus, figure (i) is traversable.

(ii)

Node	A	B	C	D	E
Order of node	2	2	2	2	2

Number of odd nodes = 0

Number of even nodes = 5

Since the figure has only even nodes, it satisfies the condition of traversability

Thus, figure (ii) is traversable.

(iii)

Node	A	B	C	D
Order of node	3	3	3	3

Number of odd nodes = 4

Number of even nodes = 0

Since the figure has more than two odd nodes, it does not satisfy the condition of traversability.

Thus, figure (iii) is not traversable.

(iv)

Node	A	B	C	D	E	F
Order of node	2	4	2	4	2	2

Number of odd nodes = 0

Number of even nodes = 6

Since the figure has only even nodes, it satisfies the condition of traversability

Thus, figure (iv) is traversable.

(v)

Node	A	B	C	D	E	F	G
Order of node	4	3	3	4	4	4	4

Number of odd nodes = 2

Number of even nodes = 5

Since the figure has only 2 odd nodes, it satisfies the condition of traversability.

Thus, figure (v) is traversable.

(vi)

Node	A	B	C	D	E	F
Order of node	2	3	3	2	3	3

Number of odd nodes = 4

Number of even nodes = 2

Since the figure has more than two odd nodes, it does not satisfy the condition of traversability.

Thus, figure (vi) is not traversable.