**6. Comparisons and Discussion**

**Table 2.** Comparison

 of all indices for

• Firstly, we have obtained some indices of *HAC*5*C*7[*p*, *q*] Nanotube for any *p* and *q*. Now from Table 2, it can be seen that all indices are in increasing order as the values of *p*, *q* increase. Finally, we depicted the the graphical representation of *HAC*5*C*7[*p*, *q*] Nanotube for hyper Zagreb index, first and second multiple Zagreb index in Figure 7 and for first and second Zagreb polynomial in Figure 8.

**[***p***,** *q***]** *HM***(***G***)** *PM***1(***G***)** *PM***2(***G***)** [1, 1] 2796 2.11 × 10<sup>11</sup> 3.4 × 10<sup>15</sup> [2, 2] 13, 368 3.31 × 10<sup>25</sup> 4.5 × 10<sup>28</sup> [3, 3] 31, 716 4.21 × 10<sup>55</sup> 6.61 × 10<sup>62</sup> [4, 4] 57, 840 6.57 × 10<sup>95</sup> 8.72 × 10<sup>98</sup>

*HAC*5*C*7[*p*, *q*] Nanotube.

**Figure 7.** (**a**) Hyper Zagreb index; (**b**) First multiple Zagreb index; (**c**) Second multiple Zagreb index.

**Figure 8.** (**a**) First Zagreb polynomial; (**b**) Second multiple Zagreb polynomial.

• Secondly, we have worked out many indices of *HAC*5*C*6*C*7[*p*, *q*] Nanotube for each *p* and *q*. Now from Table 3, we can easily see that all indices are in increasing order as the values of *p*, *q* increase. Finally, we gave the the graphical representation of *HAC*5*C*6*C*7[*p*, *q*] Nanotube for hyper Zagreb index, first and second multiple Zagreb index in Figure 9 and for first and second Zagreb polynomial in Figure 10.


**Table 3.** Comparison of all indices for *HAC*5*C*6*C*7[*p*, *q*] Nanotube.

**Figure 9.** (**a**) Hyper Zagreb index; (**b**) First multiple Zagreb index; (**c**) Second multiple Zagreb index.

**Figure 10.** (**a**) First Zagreb polynomial; (**b**) Second multiple Zagreb polynomial.

• Now, we have worked out various indices of *KTUC*[*p*, *q*],(*p*, *q* ≥ 1) Nanotorus with different *p* and *q*. Now from Table 4, we have that each index increases with the values of *p*, *q* increasing. Finally, we depicted the the graphical representation of *KTUC*[*p*, *q*],(*p*, *q* ≥ 1) Nanotorus for hyper Zagreb index, first and second multiple Zagreb index in Figure 11 and for first and second Zagreb polynomial in Figure 12.

**Table 4.** Comparison of all indices for *KTUC*[*p*, *q*],(*p*, *q* ≥ 1) Nanotorus.


**Figure 11.** (**a**) Hyper Zagreb index; (**b**) First multiple Zagreb index; (**c**) Second multiple Zagreb index.

**Figure 12.** (**a**) First Zagreb polynomial; (**b**) Second multiple Zagreb polynomial.

• At the end of this section, we have computed substantial indices of *GTUC*[*p*, *q*],(*p*, *q* ≥ 1) Nanotube for different values of *p*, *q*. Now from Table 5, it can be seen that all indices are in increasing order as the values of *p*, *q* increase. We also provided the the graphical representation of *GTUC*[*p*, *q*],(*p*, *q* ≥ 1) Nanotube for hyper Zagreb index, first and second multiple Zagreb index in Figure 13 and for first and second Zagreb polynomial in Figure 14.

**Table 5.** Comparison of all indices for *GTUC*[*p*, *q*],(*p*, *q* ≥ 1) Nanotube.

**Figure 13.** (**a**) Hyper Zagreb index; (**b**) First multiple Zagreb index; (**c**) Second multiple Zagreb index.

**Figure 14.** (**a**) First Zagreb polynomial; (**b**) Second multiple Zagreb polynomial.
