• **Entropy related to** *ABC* **index**

Let *<sup>μ</sup>*((*ai*)(*aj*)) = *Vai* +*Vaj* −2 *Va*˙ *i* ×*Va*˙ *j* . Then *ABC* index (1) is given by

$$ABC\_G \quad = \sum\_{a\_i, a\_j \in \mathbb{F}\_G} \left\{ \sqrt{\frac{V\_{a\_i} + V\_{a\_j} - 2}{V\_{a\_i} \times V\_{a\_j}}} \right\} = \sum\_{a\_i, a\_j \in \mathbb{F}\_G} \mu\left( (a\_i)(a\_j) \right).$$

Adding the parameters of *ABCG* into Equation (5), then the atom–bond connectivity (*ENTABC*) entropy is

$$ENT\_{ABC\_G} = \log\left(ABC\_G\right) - \frac{1}{ABC\_G} \log\left\{ \prod\_{a\_i a\_j \in \mathbb{F}\_G} \left( \sqrt{\frac{V\_{a\_i} + V\_{a\_j} - 2}{V\_{a\_i} \times V\_{a\_j}}} \right) \begin{pmatrix} \sqrt{\frac{V\_{a\_i} + V\_{b\_j} - 2}{V\_{a\_i} \times V\_{b\_j}}}\\ \end{pmatrix} \right\} \tag{6}$$
