From what I've read, symmetry seems to play a very important role in determining melting point, which higher symmetry often leading to higher melting points, all other things equal. Your drawing is consistent with this. There's an entropic reason for that. If you think in terms of freezing points, freezing requires crystallization more or less, with molecules lining up just so. If a molecule is more symmetric, there are more ways for molecules to line up in the same mutual orientations, which makes it easier to crystallize, which means it happens at higher temperatures (because it is more favorable to be in a solid phase). It's not a hard and fast rule, but it's usually a decent bet that if two molecules have the same chemical formula, the one with the higher symmetry will have the higher melting point. "More branched" is a poor-man's way of saying "lower symmetry", so this is why higher branching often have lower melting point... but if the molecular weight is small, "more branched" can also mean higher symmetry, as in the case here of your 2,2-dimethyl propane. So considering symmetry is better than considering branching.