• **Hyper Zagreb index of** *HAC***5***C***7[***p***,** *q***] Nanotube**

Let *G* be the *HAC*5*C*7[*p*, *q*] Nanotube. Then by Equations (1), we have

$$\begin{split} HM(G) &= \sum\_{sr \in E(G)} \left[ dgr(s) + dgr(r) \right]^2 \\ HM(G) &= \sum\_{sr \in E\_1} \left[ dgr(s) + dgr(r) \right]^2 + \sum\_{sr \in E\_2} \left[ dgr(s) + dgr(r) \right]^2 + \sum\_{sr \in E\_3} \left[ dgr(s) + dgr(r) \right]^2 \\ &+ \sum\_{sr \in E\_4} \left[ dgr(s) + dgr(r) \right]^2 + \sum\_{sr \in E\_5} \left[ dgr(s) + dgr(r) \right]^2 + \sum\_{sr \in E\_6} \left[ dgr(s) + dgr(r) \right]^2 \\ &= 13^2 |E\_1| + 14^2 |E\_2| + 16^2 |E\_3| + 16^2 |E\_4| + 17^2 |E\_5| + 18^2 |E\_6| \\ &= 169(2p) + 196(2p) + 256p + 256p + 289(2p) + 324(12pq - 9p) = 3888pq - 1092p^2 \end{split}$$
