Table 1 Topological indices with notations and formula

First Zagreb Index [34]

M₁ (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \left( {dr + dj} \right)\)

Second Zagreb Index [34]

M₂ (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \left( {dr \times dj} \right)\)

Harmonic Index [35]

H (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \frac{2}{{\left( {dr + dj} \right)}}\)

Forgotton Index [36]

F (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} [\left( {dr} \right)^{2} + \left( {dj} \right)^{2} ]\)

Shilpa-Shanmukha Index [37]

SS (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \sqrt {\frac{dr \times dj}{{dr + dj}}}\)

Atom Bond Connectivity Index [38]

ABC (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \sqrt {\frac{dr + dj - 2}{{dr \times dj}}}\)

Randic Index [39]

RI (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \sqrt {\frac{1}{dr \times dj}}\)

Sum Connectivity Index [40]

SC (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \sqrt {\frac{1}{dr + dj}}\)

Geometric Arithmetic Index[38]

GA (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} 2\frac{{\sqrt {dr \times dj} }}{dr + dj}\)

Hyper Zagreb Index [41]

HZ (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \left( {dr + dj} \right)^{2}\)

Redefined First Zagreb Index [42]

ReZ₁ (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \frac{{\left( {dr \times dj} \right)}}{{\left( {dr + dj} \right)}}\)

Redefined Second Zagreb Index [42]

ReZ₂ (G)

\(\mathop \sum \limits_{rj \in E\left( G \right)} \left( {dr \times dj} \right)\left( {dr + dj} \right)\)