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The following is a problem from Fundamentals of Organic Chemistry by McMurry.

Draw two constitutional isomers of cis-1,2-dibromocyclopentane.

I don't get how there can be constitutional isomers for the above-mentioned compound. Constitutional isomers must have different connections. The question specifies everything including the spatial arrangement.

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If I understood you correctly, your objection is to the relative cis- designation in the name of the compound. As far as I can tell, the use of any stereochemical designation within the context of that question is either deliberately misleading, incorrect, or simply pointless. Per the definition of constitutional isomerism, the only criteria that the two molecules in your answer must satisfy is that they have (a) the same molecular formula, and (b) different structural connectivity. Stereochemistry, whether relative or absolute, is totally irrelevant. Note the wording in the IUPAC Gold Book entry for constitution (emphasis mine):

The description of the identity and connectivity (and corresponding bond multiplicities) of the atoms in a molecular entity (omitting any distinction arising from their spatial arrangement).

Hence, any molecule with the formula $\ce{C5H8Br2}$ that differs in connectivity from a cyclopentane with two vicinal bromine atoms should be a valid answer. Two such isomers are given by simply permuting the positions of the bromines (i.e., 1,1-dibromocyclopentane and 1,3-dibromocyclopentane). Of course, there are numerous other possible answers.

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