Introducing complete graphs in molecular connectivity studies

Abstract

The mathematical model of the molecular polarizability of fifty-four organic compounds, of the lattice enthalpy of twenty metal halides, and of the partition coefficient of twenty-five organic compounds has been used to test four different complete graph, K$_p$, conjectures for the core electrons of any atom with principal quantum number n g 2. Medium-sized sets of molecular connectivity and molecular pseudoconnectivity indices based on these four K$_p$ conjectures have been used as basis indices to model the three different properties of the three classes of compounds. The odd complete graph conjecture for the core electrons gives rise to an optimal model for the three properties. Within the frame of this odd complete graph conjecture two different algorithms to derive the basis indices, can be used. One algorithm defines a single-odd valence delta number, δ$^v$ (q = 1), while the other algorithm defines a double-odd valence delta number, δ$^v$ (q = p). The valence delta number, δ$^{v}$, is the main parameter of the molecular connectivity and pseudoconnectivity basis indices.