Table 2.

Formulation of molecular descriptors based on neighborhood degree sum of nodes for a graph $\Gamma$

Topological indices	Formulation
Neighborhood Zagreb index ($M_N(\Gamma )$)	$\sum _{x\in V(\Gamma )}{\kappa }_{\Gamma }{(x)}^2$
Neighborhood version of Forgotten topological index ($F_N(\Gamma )$)	$\sum _{x\in V(\Gamma )}{\kappa }_{\Gamma }{(x)}^3$
Modified neighborhood version of forgotten topological index ($F_N^{\ast }(\Gamma )$)	$\sum _{xy\in E(\Gamma )}[{\kappa }_{\Gamma }{(x)}^2+{\kappa }_{\Gamma }{(y)}^2]$
Neighborhood version of second Zagreb index ($M_2^{\ast }(\Gamma )$)	$\sum _{xy\in E(\Gamma )}[{\kappa }_{\Gamma }(x){\kappa }_{\Gamma }(y)]$
Neighborhood version of hyper Zagreb index ($H{M}_N(\Gamma )$)	$\sum _{xy\in E(\Gamma )}{[{\kappa }_{\Gamma }(x)+{\kappa }_{\Gamma }(y)]}^2$
Third version of Zagreb index ($M_1^{{}^{\prime }}(\Gamma )$)	$\sum _{xy\in E(\Gamma )}[{\kappa }_{\Gamma }(x)+{\kappa }_{\Gamma }(y)]$