Deduction and Application of Novel IHD-Like Equations for the Calculation of Covalent Bonds in Cyclic Unsaturated Molecules

Currently in order to calculate the number of covalent bonds for cyclic unsaturated organic molecules there are equations that include the index of hydrogen deficiency (IHD), a σ-bonds derivation from the Euler characteristic for planar graphs and other empirical formulations. However the IHD which is also known as the degree of unsaturation (DOU) requires to assign a numerical value for the pi(π) bonds and rings without knowing their precise number in a molecule, and all the other equations that are used to determine the numerical value of sigma(σ) and single bonds are made up of variables such as the number of rings, double and triple bonds. In this manuscript we present a novel type of mathematical model that was deduced by using chemical graph theory and can be applied to calculate the value of covalent bonds and rings for cyclic organic molecules with double or triple bonds only knowing the number of atoms, their corresponding valences and a new chemical concept which we called total unsaturation (TU) that represents the degree of unsaturation expressed as a percentage. The objective of this study is to highlight a deeper mathematical relationship formed by multiple structural elements of a molecule in order to enhance the correlations between graph theory and organic chemistry from a different perspective that is primarly focused on the number of bonds.