This paper reports densities, rho(ijk) and speeds of sound, mu(ijk) data of ternary {1-butyl-2,3-dimethylimidazolium tetrafluoroborate (i) + 1-butyl-3-methylimidazolium tetrafluoroborate or 1-ethyl-3-methylimidazolium tetrafluoroborate (j) + cyclopentanone or cyclohexanone (k)} mixtures at temperatures 293.15 K to 308.15 K using a digital densimeter and speed of sound analyser. The observed rho(ijk) and mu(ijk) data have been employed to determine excess molar volumes, V-ijk(E) and excess isentropic compressiblities, (K-S(E))(ijk) respectively of the studied mixtures. The topology of the constituent molecules (Graph theory) of the binary ionic liquid mixtures has recently been utilized (Gupta et al., 2016) to predict their V-E, K-S(E), HE and CpE data. In the present studies, the topology of the components of the ternary mixtures (comprise of two ionic liquids and one organic solvent) has been employed (Graph theory) to obtain expressions for V-ijk(E) and (K-S(E))(ijk) data that describe well the measured V-ijk(E) and (K-S(E))(ijk) values. The observed V-ijk(E) and (K-S(E))ijk values have also been tested in terms of Prigogine-Flory-Patterson (PFP) theory. It has been observed that V-ijk(E) and (K-S(E))(ijk) values predicted by Graph theory are comparable with the experimental values. (C) 2017 Elsevier Ltd.