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Is it possible to express the extent to which an alkane has branching (branch count)?

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Your question is a bit unclear as to what exactly you are wondering. However, for a simple saturated hydrocarbon what's IUPAC name is given, its base name is given by the largest chain. Knowing this, all branching is indicated by the named substituents that branch off of this main chain.

For example, 2,3,5-trimethylhexane will be a 6-carbon saturated chain with 3 branches. Hopefully this helps answer your question, maybe you can add some clarification?

2,3,5-trimethylhexane

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