Question

Find the number of nodes, arcs and regions in the following networks.

(i)

(ii)

(iii)

(iv)

Answer 1

(i)

In this graph A, B and C are nodes.

AB, BA, AC and BC are arcs.

The regions are the area within the circle AB, area within ABC and the area outside ABC.

Number of nodes = N = 3

Number of arcs = A = 4

Number of regions = R = 3

(ii)

In this graph A, B and C are nodes.

AB (straight path), BC (straight path), AB (curved path), BC ( curved path) and AC are arcs.

The regions are the areas coloured red, blue, green and the area outside them.

Number of nodes = N = 3

Number of arcs = A = 5

Number of regions = R = 4

(iii)

In this graph, P, Q, R and S are nodes.

PQ, QP, QR, RQ,PS,QS and RS are arcs.

The regions are the area within the circle AB, the area within the circle QR, the area within PSQ, the area within RSQ and the area outside PSR.

Number of nodes = N = 4

Number of arcs = A = 7

Number of regions = R = 5

(iv)

In this graph, A, B, C and D are nodes.

AB, BC, CD, DA (straight path) and AB, BC, CD, DA (curved path) are arcs.

The regions are the areas coloured red, blue, green, pink and yellow and the area outside them.

Number of nodes = N = 4

Number of arcs = A = 8

Number of regions = R = 6