Question

Do cis and trans isomers have the same structural connectivity?

Answer 1

Absolutely; this is why they are considered GEOMETRIC isomers.

Explanation:

Let's take the simple example of 2-butene.`H_3C-CH=CH-CH_3`. Clearly, there is a cis -isomer, and a trans -isomer. (I would post pictures but my google-fu is weak.)

IN BOTH isomers, `C1` is connected to `C2` is connected to `C3` is connected to `C4`. So the gross carbon connectivity is IDENTICAL. Nevertheless, the spatial geometry of each isomer is different, and this gives rise to different physical properties, and different chemical properties.