• **Multiple Zagreb indices of** *HAC***5***C***7[***p***,** *q***] Nanotube**

Let *G* be the *HAC*5*C*7[*p*, *q*] Nanotube. Then by Equations (2) and (3), we have

$$\begin{split} PM\_{1}(G) &= \prod\_{sr \in E(G)} [\operatorname{dgr}(s) + \operatorname{dgr}(r)] \\ PM\_{1}(G) &= \prod\_{sr \in E\_{1}} [\operatorname{dgr}(s) + \operatorname{dgr}(r)] \times \prod\_{sr \in E\_{2}} [\operatorname{dgr}(s) + \operatorname{dgr}(r)] \times \prod\_{sr \in E\_{3}} [\operatorname{dgr}(s) + \operatorname{dgr}(r)] \\ &\times \prod\_{sr \in E\_{4}} [\operatorname{dgr}(s) + \operatorname{dgr}(r)] \times \prod\_{sr \in E\_{5}} [\operatorname{dgr}(s) + \operatorname{dgr}(r)] \times \prod\_{sr \in E\_{6}} [\operatorname{dgr}(s) + \operatorname{dgr}(r)] \\ &= 13^{|E\_{1}|} \times 14^{|E\_{2}|} \times 16^{|E\_{3}|} \times 16^{|E\_{4}|} \times 17^{|E\_{5}|} \times 18^{|E\_{6}|} \\ &= 13^{2p} \times 14^{2p} \times 16^{p} \times 16^{p} \times 17^{2p} \times 18^{|12p - 9p|} \end{split}$$

$$\begin{array}{rcl} PM\_2(G) &=& \prod\_{sr \in E(G)} \left[ dgr(s) \times dgr(r) \right] \\ PM\_2(G) &=& \prod\_{sr \in E\_1} \left[ dgr(s) \times dgr(r) \right] \times \prod\_{sr \in E\_2} \left[ dgr(s) \times dgr(r) \right] \times \prod\_{sr \in E\_3} \left[ dgr(s) \times dgr(r) \right] \\ & \times \prod\_{sr \in E\_4} \left[ dgr(s) \times dgr(r) \right] \times \prod\_{sr \in E\_5} \left[ dgr(s) \times dgr(r) \right] \times \prod\_{sr \in E\_6} \left[ dgr(s) \times dgr(r) \right] \\ &=& 42^{|E\_1|} \times 48^{|E\_2|} \times 63^{|E\_3|} \times 64^{|E\_4|} \times 72^{|E\_5|} \times 81^{|E\_6|} \\ &=& 42^{2p} \times 48^{2p} \times 63^p \times 64^p \times 72^{2p} \times 81^{(12p - 9p)} \end{array}$$
