Question

derivation for CnH2n ​

Answer 1

Let the alkane considered possess n carbon atoms and h hydrogen atoms. The

molecular graph of such an alkane is a tree with n + h vertices, and thus (by

Theorem 2) with n + h − 1 edges.

For chemical reasons the degrees of the vertices representing carbon atoms

are equal to four, and the degrees of the vertices representing hydrogen atoms are

equal to one. (Ask your chemistry teacher to explain you why this is so; this has

something to do with the valency of carbon and hydrogen.)

Since there are n vertices of degree 4, and h vertices of degree one, the sum on

the left-hand side of (1) is equal to 4 × n + 1 × h, which results in:

4n + h = 2(n + h − 1) .

By simple rearrangements (which the reader should do himself), from this equality

follows

h = 2n + 2

as required by the CnH2n+2 formula