Isomers for alkynes

Alkynes are unsaturated hydrocarbons that have one or more carbon-carbon triple bonds.   Alkynes with four carbons or more exist as more than one constitutional isomer. A constitutional isomer is a compound with the same molecular formula but a different atom-to-atom bonding sequence.

The different atom-to-atom bonding sequence may be due
to a difference in the carbon skeleton (as seen for alkanes) or
to a difference in the position of the triple bond
 
CCCC
C ≡ C – C – C
C – C ≡ C – C
Consider a linear C4 skeleton that has two different bonding environments for carbon (red and blue). 
A triple bond can be between a red carbon and a blue carbon OR between two blue carbons.
There are therefore two possible alkyne constitutional isomers for this carbon skeleton.

The number of alkyne constititonal isomers for a particular carbon skeleton depends on
the number of different bonding environments for carbon AND
the number of adjacent pairs of carbon atoms where both are involved in one or fewer bonds to other carbon atoms

This means that neither of the triply-bonded carbons can one that bears a branch!!

When assessing the number of different bonding environments, it is important to realise that 
any linear chain is symmetrical about its centre,
thus bonding enviroments for carbon are the same to the left and the right of the centre.
Thus there is only one isomer above with a double bond between red and blue carbons. 
 
        C
     |
C —  C — C — C C 

the presence of a branch affects the number of different bonding environments 

Branches of the same composition bonded to the same carbon are equivalent.
The ends of the chain may no longer be equivalent.
See the number of bonding environments for carbon in the carbon skeleton shown