Transmembrane β-barrel proteins are a special class of transmembrane proteins which play several key roles in human body and diseases. Due to experimental difficulties, the number of transmembrane β-barrel proteins with known structures is very small. Over the years, a number of learning-based methods have been introduced for recognition and structure prediction of transmembrane β-barrel proteins. Most of these methods emphasize on homology search rather than any biological or chemical basis. We present a novel graph-theoretic model for classification and structure prediction of transmembrane β-barrel proteins. This model folds proteins based on energy minimization rather than a homology search, avoiding any assumption on availability of training dataset. The ab initio model presented in this paper is the first method to allow for permutations in the structure of transmembrane proteins and provides more structural information than any known algorithm. The model is also able to recognize β-barrels by assessing the pseudo free energy. We assess the structure prediction on 41 proteins gathered from existing databases on experimentally validated transmembrane β-barrel proteins. We show that our approach is quite accurate with over 90% F-score on strands and over 74% F-score on residues. The results are comparable to other algorithms suggesting that our pseudo-energy model is close to the actual physical model. We test our classification approach and show that it is able to reject α-helical bundles with 100% accuracy and β-barrel lipocalins with 97% accuracy. We show that it is possible to design models for classification and structure prediction for transmembrane β-barrel proteins which do not depend essentially on training sets but on combinatorial properties of the structures to be proved. These models are fairly accurate, robust and can be run very efficiently on PC-like computers. Such models are useful for the genome screening.