Question

Verify Euler’s formula for the following graphs.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Answer 1

Graph	Number of Nodes N	Number of Regions R	Number of Arcs A	N + R	A + 2
	4	3	5	4 + 3	5 + 2
	4	4	6	4 + 4	6 + 2
	6	5	9	6 + 5	9 + 2
	4	3	5	4 + 3	5 + 2
	5	9	12	5 + 9	12 + 2
	8	6	12	8 + 6	12 + 4

It can be observed in each figure that N + R = A + 2.

Hence, Euler’s formula is verified for each case.