• **Entropy related to** *ABS* **index**

Let *<sup>μ</sup>*((*ai*)(*aj*)) = *Vai* +*Vaj* −2 *Vai* +*Vaj* . Then the *ABS* index (2) is given by

$$ABS\_G \quad = \sum\_{a\_i, a\_j \in \xi\_G} \left\{ \sqrt{\frac{V\_{a\_i} + V\_{a\_j} - 2}{V\_{a\_i} + V\_{a\_j}}} \right\} = \sum\_{a\_i, a\_j \in \xi\_G} \mu((a\_i)(a\_j)). \tag{7}$$

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

$$ENT\_{ABS\_G} = \log\left(ABS\_G\right) - \frac{1}{ABS\_G} \log \left\{ \prod\_{a\_i a\_j \in \mathbb{F}\_G} \left( \sqrt{\frac{V\_{a\_i} + V\_{a\_j} - 2}{V\_{a\_i} + V\_{a\_j}}} \right)^{\left(\sqrt{\frac{V\_{a\_i} + V\_{a\_j} - 2}{V\_{a\_j} + V\_{a\_j}}}\right)} \right\}.\tag{8}$$

#### • **Entropy related to Albertson index**

Let *<sup>μ</sup>*((*ai*)(*aj*)) = |*Vai* − *Vaj* | . Then the Alberston entropy (3) is given by

$$A\_{(G)} \quad = \sum\_{a\_i, a\_j \in \mathbb{F}\_G} \left\{ |V\_{a\_i} - V\_{a\_j}| \right\} = \sum\_{a\_i, a\_j \in \mathbb{F}\_G} \mu((a\_i)(a\_j)).$$

Adding the parameters of *A*(*G*) into Equation (5), then the Alberston (*ENTA*)) entropy is

$$ENT\_{A\_{(G)}} = \log\left(A\_{(G)}\right) - \frac{1}{A\_{(G)}} \log \left\{ \prod\_{a\_i, a\_j \in \mathbb{F}\_{\mathcal{G}}} \left( |V\_{a\_i} - V\_{a\_j}| \right)^{\left( \left| V\_{a\_i} - V\_{a\_j} \right| \right)} \right\}.\tag{9}$$
