Table 1 Notation and formulas of the reverse degree based indices.
From: Modeling and estimation of physiochemical properties of cancer drugs using entropy measures
Name of Index | Notation | Formula | Formula expansion |
|---|---|---|---|
Randić \(\alpha =-1, \frac{-1}{2}, 1, \frac{1}{2}\) | \(R_{\alpha }(Z)\) | \(\sum _{rs\in E (Z)} \mathscr {F}_{ R_{\alpha }}(rs)\) | \(\sum _{rs\in E (Z)} ({\Upsilon }_r\times {\Upsilon }_s)^\alpha\) |
Atom bond connectivity | ABC(Z) | \(\sum _{rs\in E (Z)} \mathscr {F}_{ABC}(rs)\) | \(\sum _{rs\in E (Z)}\sqrt{\frac{{\Upsilon }_r+{\Upsilon }_s-2}{{\Upsilon }_r\times {\Upsilon }_s}}\) |
Geometric arithmetic | GA(Z) | \(\sum _{rs\in E (Z)} \mathscr {F}_{GA}(rs)\) | \(\sum _{rs\in E (Z)} \frac{2\sqrt{{{\Upsilon }_r\times {\Upsilon }_s}}}{{{\Upsilon }_r+ {\Upsilon }_s}}\) |
First Zagreb | \(M_1 (Z)\) | \(\sum _{rs\in E (Z)} \mathscr {F}_{M_1}(rs)\) | \(\sum _{rs\in E (Z)}({\Upsilon }_r+{\Upsilon }_s)\) |
Second Zagreb | \(M_2 (Z)\) | \(\sum _{rs\in E (Z)} \mathscr {F}_{M_2}(rs)\) | \(\sum _{rs\in E (Z)}({\Upsilon }_r\times {\Upsilon }_s)\) |
Hyper Zagreb | HM(Z) | \(\sum _{rs\in E (Z)} \mathscr {F}_{HM}(rs)\) | \(\sum _{rs\in E (Z)}({\Upsilon }_r+{\Upsilon }_s)^2\) |
Forgotten | F(Z) | \(\sum _{rs\in E (Z)} \mathscr {F}_{F}(rs)\) | \(\sum _{rs\in E (Z)}[({\Upsilon }_r)^2+({\Upsilon }_s)^2]\) |
Augmented Zagreb | AZI(Z) | \(\sum _{rs\in E (Z)} \mathscr {F}_{AZI}(rs)\) | \(\sum _{rs\in E (Z)} (\frac{{\Upsilon }_r\times {\Upsilon }_s}{{\Upsilon }_r+ {\Upsilon }_s-2})^3\) |
Balaban | J(Z) | \(\sum _{rs\in E (Z)} \mathscr {F}_{J}(rs)\) | \(\sum _{rs\in E (Z)} (\frac{q}{q-p+2}\times \frac{1}{\sqrt{{\Upsilon }_r\times {\Upsilon }_s}})\) |
Redefined first Zagreb | \(ReZG_1 (Z)\) | \(\sum _{rs\in E (Z)} \mathscr {F}_{ReZG_1}(rs)\) | \(\sum _{rs\in E (Z)}\frac{{\Upsilon }_r+{\Upsilon }_s}{{\Upsilon }_r\times {\Upsilon }_s}\) |
Redefined second Zagreb | \(ReZG_2 (Z)\) | \(\sum _{rs\in E (Z)} \mathscr {F}_{ReZG_2}(rs)\) | \(\sum _{rs\in E (Z)}\frac{{\Upsilon }_r\times {\Upsilon }_s}{{\Upsilon }_r+{\Upsilon }_s}\) |
Redefined third Zagreb | \(ReZG_3 (Z)\) | \(\sum _{rs\in E (Z)} \mathscr {F}_{ReZG_3}(rs)\) | \(\sum _{rs\in E (Z)}({\Upsilon }_r\times {\Upsilon }_s)({\Upsilon }_r+ {\Upsilon }_s)\) |
