Identifying the number of constitutional isomers

saturated
hydrocarbons
C2H6
C3H8
C4H10
C5H12
Saturated hydrocarbons have the maximum number of hydrogens for that number of carbons. These are known as alkanes and have the general formula CnH2n+2.

Hydrocarbons having a carbon-carbon double bond are unsaturated because they have two fewer than the maximum number of hydrogens for a given number of carbon atoms. These hydrocarbons are known as alkenes and have the general formula CnH2n.

Alkene constitutional isomers may differ in the arrangement of the carbon atoms and/or the position of the double bond.  When predicting the number of possible isomers for a given carbon skeleton, it is important take into consideration both the symmetry of the carbon skeleton and the number of bonds to individual carbons as outlined below.

POINT 1:  Some carbons in the carbon skeleton may be equivalent due to being in the same bonding environment).
Equivalent atoms are bonded to the same number and type of atoms/groups.

For compounds with a linear arrangement of carbons, the chain is symmetrical about its center.
The center of a chain may be a bond (as for C4 below) or a carbon (as for C-C-C-C-C).
 

C = C – C – C
C – C = C – C
A C4 chain has only two carbons in different bonding environments. 
The red carbons are bonded to 3H and CH2CH2CH3.
The blue carbons are bonded to 2H and one CH3 and one CH2CH3.

The only two possible alkenes having this arrangement of carbons have a double bond in one case between a red and blue pair, and in the other case between a pair of blues.

Branches of identical composition are in the same bonding environment IF they are attached to the same carbon.
C
 |
 C = C — C


There is only one C4 branched alkene isomer (2-methylpropene) because each pair of adjacent carbons is the same (red and blue).

The non-equivalent carbons in one of the possible C6 carbon skeletons are shown in different colours.
Think about the number of different pairs of adjacent carbons where each carbon has at least 1H in the alkane. 
That is equal to the number of double bond isomers for this carbon skeleton.
 
Point 2:  Doubly-bonded carbons may be each bonded to a maximum of two carbons
The pink carbon in the C6 carbon skeleton is bonded to three carbons and can not be involved in a double bond.