How many open-chain alkenes (one C=C, no rings) of molecular formula $\mathrm{C}{}_6\mathrm{H}{}_{12}$ exist if only structural isomers are counted (cis/trans isomers are not counted separately)? Give an integer.

Group by carbon skeleton. Hexane skeleton: hex-1-ene, hex-2-ene, hex-3-ene (3); 2-Methylpentane skeleton: 2-methylpent-1-ene, 2-methylpent-2-ene, 4-methylpent-1-ene, 4-methylpent-2-ene (4); 3-Methylpentane skeleton: 3-methylpent-1-ene, 3-methylpent-2-ene, 2-ethylbut-1-ene (3); 2,2-Dimethylbutane skeleton: 3,3-dimethylbut-1-ene (1); 2,3-Dimethylbutane skeleton: 2,3-dimethylbut-1-ene, 2,3-dimethylbut-2-ene (2). Total 3 + 4 + 3 + 1 + 2 = 13, verified by computer enumeration of all acyclic C6H12 structures.