The densities rho speeds of sound u, and molar heat capacities C-p of tetrahydropyran or 1,4-dioxane (1) + cyclohexanone or cycloheptanone (2) mixtures at 293.15, 298.15, 303.15, and 308.15 K, and excess molar enthalpies, H-E at 308.15 K and atmospheric pressure 0.1 MPa have been measured over the entire composition range. The excess molar volumes V-E, excess isentropic compressibilities kappa(E)(S) and excess heat capacities, C-P(E) of the studied mixtures have been determined using the measured experimental data. The observed V-E, kappa(E)(S), H-E, and C-P(E) data have been tested in terms of graph theory. The analyses of V-E data by graph theory suggest that while tetrahydropyran or 1,4-dioxane exists as a mixture of monomer and dimer; cyclohexanone or cycloheptanone exists as a mixture of open and cyclic dimer. Further, (1 + 2) mixtures are characterized by interactions between oxygen atom/s and hydrogen atom of tetrahydropyran or 1,4-dioxane with hydrogen atom/s and oxygen atom of cyclohexanone or cycloheptanone. The quantum mechanical calculations and analysis of IR spectral data of (1 + 2) mixtures also support this viewpoint. It has been observed that graph theory correctly predicts the V-E, kappa(E)(S), H-E, and C-P(E) data of the present mixtures.