Three newly defined information theoretic topological indices, namely “degree complexity (Id),” “graph vertex complexity (HV),” and “graph distance complexity (HD)” along with three other information indices have been used to study their discriminating power of 45 trees and 19 monocyclic graphs. It is found that the newly defined indices have satisfactory discriminating power while HD has been found to be the only index to discriminate all the graphs studied.

Nucleotide composition and distribution along a DNA sequence is known to play a vital role in the determination of gene functions. Protein coding regions, regulatory sequences, and other functional regions are determined generally by homology studies with comparable genes from other species or specific experimental verification. With the rapid and explosive increase in sequence information, new computational techniques for rapid determination of such information and comparative studies of different genes are becoming necessary which ideally should encompass not only DNA sequences but other macromolecular sequences as well.

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A database of primary sequences of 28 immunogenic peptides, known to elicit T cell response, derived from five different haplotypes was compiled to identify allele specific helper T cell antigenic sites using a rule based graph-theoretical method. The prediction was based on the identification of allele specific patterns in the form of "topological shape and size" present in the peptides. Indices computed from weighted connected graph models of amino acid side chains and peptides were used in this purpose. The system was trained by 10 Ad and 10 non-Ad restricted peptide sequences, assigned actives and inactives, respectively, chosen randomly from the database, and four Ad and four non-Ad restricted sequences were kept as test peptides. This allowed the system to learn about "topological shape and size" specific for Ad restricted peptides from the differences, if any, they had with the inactive peptides in that respect. The system made 100% correct prediction for the training set peptides and misclassified only one inactive peptide of the test set. The system also identified crucial residues for lambda repressor 12-24 and insulin A-chains. This identification also shows that activity related/crucial residues could be located at varying distances from the peptide terminals. To our knowledge, the method is unique of its kind in the literature and may find application in the rational design of synthetic vaccines and other peptides of immunological importance.