Excess molar enthalpies, H-ijk(E) of 1-ethyl-3-methylimidazolium tetrafluoroborate (i) + 2-methylaniline (j)+ pyridine or alpha- or beta- or gamma-picoline (k) ternary mixtures have been measured over an entire mole fraction at 298.15 K using micro differential scanning calorimeter [Model-mu, DSC 7 Evo]. The Redlich-Kister equation parameters have been fitted to measured data. The H-ijk(E) values for the studied mixtures are negative over entire composition range. The topology of the constituents of the mixtures has been utilized to (Graph theory) predict It, values of the investigated mixtures. It has been observed that H-ijk(E) values determined by Graph theory compare well with their corresponding experimental values. (C) 2013 Elsevier B.V. All rights reserved.