Full article: Correction

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Article title: Multiplicative Topological Indices of Molecular Structure in Anticancer Drugs

Authors: Shao, Z., Jahanbani, A., & Sheikholeslami, S. M.

Journal: Polycyclic Aromatic Compounds

DOI: http://dx.doi.org/10.1080/10406638.2020.1743329

The authors calculated certain degree-based topological indices of molecular structure of anticancer drugs. But, the above published article had computational errors in the given result. In below notes, the correct versions of the aforementioned erroneous are expressed.

The original article has also now been re-published with the corrections updated.

1. The equations under Theorem 1 have been corrected as below: ${SCII (S P [n]) = (\frac{\sqrt{6}}{6})}^{18 n} \times {(\frac{\sqrt{7}}{7})}^{n} {(\frac{1}{2})}^{14 n + 5} \times {(\frac{\sqrt{5}}{5})}^{19 n - 1} {\times (\frac{\sqrt{3}}{3})}^{2 n + 1}$ ${RCII (S P [n]) = (\frac{1}{3})}^{16 n} \times {(\frac{\sqrt{2}}{4})}^{2 n} \times {(\frac{\sqrt{3}}{6})}^{n} \times {(\frac{1}{2})}^{6 n + 4} {\times (\frac{\sqrt{6}}{6})}^{18 n - 1} \times {(\frac{\sqrt{2}}{2})}^{2 n + 1} \times {(\frac{\sqrt{3}}{3})}^{9 n + 1} .$
2. The equations in page 6 & 7, have been corrected as below:

$CII (S P [n]) = \prod_{uvєE (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} = \prod_{u v є E_{3} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} \times \prod_{u v є E_{3}^{*} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} \times \prod_{u v є E_{6}^{*} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} \times \prod_{u v є E_{8}^{*} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} \times \prod_{u v є E_{9}^{*} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}} \times \prod_{u v є E_{7}^{*} (S P [n])} \frac{1}{\sqrt{d (u) + d (v)}}$ $= \prod_{u v є E_{3} (S P [n])} \frac{1}{\sqrt{1 + 2}} \times \prod_{u v є E_{3}^{*} (S P [n])} \frac{1}{\sqrt{1 + 3}} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{1 + 4}} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{2 + 2}} \times \prod_{u v є E_{6}^{*} (S P [n])} \frac{1}{\sqrt{2 + 3}} \times \prod_{u v є E_{8}^{*} (S P [n])} \frac{1}{\sqrt{2 + 4}} \times \prod_{u v є E_{9}^{*} (S P [n])} \frac{1}{\sqrt{3 + 3}} \times \prod_{u v є E_{7}^{*} (S P [n])} \frac{1}{\sqrt{3 + 4}}$

$= {(\frac{1}{\sqrt{3}})}^{(2 n + 1)} \times {(\frac{1}{2})}^{(9 n + 1)} \times {(\frac{1}{\sqrt{5}})}^{n} \times {(\frac{1}{2})}^{(5 n + 4)} \times {(\frac{1}{\sqrt{5}})}^{(18 n - 1)} \times {(\frac{1}{\sqrt{6}})}^{2 n} \times {(\frac{1}{\sqrt{6}})}^{16 n} \times {(\frac{1}{\sqrt{7}})}^{n} = {(\frac{\sqrt{6}}{6})}^{18 n} \times {(\frac{\sqrt{7}}{7})}^{n} {(\frac{1}{2})}^{14 n + 5} \times {(\frac{\sqrt{5}}{5})}^{19 n - 1} {\times (\frac{\sqrt{3}}{3})}^{2 n + 1} .$ $RCII (S P [n]) = \prod_{uvєE (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} = \prod_{u v є E_{3} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} \times \prod_{u v є E_{3}^{*} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} \times \prod_{u v є E_{6}^{*} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} \times \prod_{u v є E_{8}^{*} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} \times \prod_{u v є E_{9}^{*} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}} \times \prod_{u v є E_{7}^{*} (S P [n])} \frac{1}{\sqrt{d (u) \times d (v)}}$ $= \prod_{u v є E_{3} (S P [n])} \frac{1}{\sqrt{1 \times 2}} \times \prod_{u v є E_{3}^{*} (S P [n])} \frac{1}{\sqrt{1 \times 3}} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{1 \times 4}} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \frac{1}{\sqrt{2 \times 2}} \times \prod_{u v є E_{6}^{*} (S P [n])} \frac{1}{\sqrt{2 \times 3}} \times \prod_{u v є E_{8}^{*} (S P [n])} \frac{1}{\sqrt{2 \times 4}} \times \prod_{u v є E_{9}^{*} (S P [n])} \frac{1}{\sqrt{3 \times 3}} \times \prod_{u v є E_{7}^{*} (S P [n])} \frac{1}{\sqrt{3 \times 4}}$ $= {(\frac{1}{\sqrt{2}})}^{(2 n + 1)} \times {(\frac{1}{\sqrt{3}})}^{(9 n + 1)} \times {(\frac{1}{2})}^{n} \times {(\frac{1}{2})}^{(5 n + 4)} \times {(\frac{1}{\sqrt{6}})}^{(18 n - 1)} \times {(\frac{1}{\sqrt{8}})}^{2 n} \times {(\frac{1}{3})}^{16 n} \times {(\frac{1}{\sqrt{12}})}^{n}$ ${= (\frac{1}{3})}^{16 n} \times {(\frac{\sqrt{2}}{4})}^{2 n} \times {(\frac{\sqrt{3}}{6})}^{n} \times {(\frac{1}{2})}^{6 n + 4} {\times (\frac{\sqrt{6}}{6})}^{18 n - 1} \times {(\frac{\sqrt{2}}{2})}^{2 n + 1} \times {(\frac{\sqrt{3}}{3})}^{9 n + 1} .$

3. The equations under Theorem 2 have been corrected as below: ${ABCII (S P [n]) = (\frac{2}{3})}^{16 n} \times {(\frac{\sqrt{5}}{4})}^{n} {\times (\frac{\sqrt{2}}{2})}^{27 n + 4} \times {(\frac{\sqrt{6}}{3})}^{9 n + 1}$ ${GAII (S P [n]) = (\frac{2 \sqrt{2}}{3})}^{2 n} \times {(\frac{16 \sqrt{3}}{35})}^{n} {\times (\frac{2 \sqrt{6}}{5})}^{18 n - 1} {\times (\frac{\sqrt{3}}{2})}^{9 n + 1} \times {(\frac{2 \sqrt{6}}{3})}^{2 n + 1} .$
4. The equations in page 8 & 9, have been corrected as below: $ABCII (S P [n]) = \prod_{uvєE (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}} = \prod_{u v є E_{3} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}} \times \prod_{u v є E_{3}^{*} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}} \times \prod_{u v є E_{6}^{*} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{\sqrt{d (u) \times d (v)}}} \times \prod_{u v є E_{8}^{*} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}} \times \prod_{u v є E_{9}^{*} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}} \times \prod_{u v є E_{7}^{*} (S P [n])} \sqrt{\frac{d (u) + d (v) - 2}{d (u) \times d (v)}}$ $= \prod_{u v є E_{3} (S P [n])} \sqrt{\frac{1}{2}} \times \prod_{u v є E_{3}^{*} (S P [n])} \sqrt{\frac{2}{3}} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \sqrt{\frac{3}{4}} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \sqrt{\frac{1}{2}} \times \prod_{u v є E_{6}^{*} (S P [n])} \sqrt{\frac{1}{2}} \times \prod_{u v є E_{8}^{*} (S P [n])} \sqrt{\frac{1}{2}} \times \prod_{u v є E_{9}^{*} (S P [n])} \sqrt{\frac{4}{9}} \times \prod_{u v є E_{7}^{*} (S P [n])} \sqrt{\frac{5}{12}}$ $= {(\frac{1}{\sqrt{2}})}^{(2 n + 1)} \times {(\sqrt{\frac{2}{3}})}^{(9 n + 1)} \times {(\sqrt{\frac{3}{4}})}^{n} \times {(\sqrt{\frac{1}{2}})}^{(5 n + 4)} \times {(\sqrt{\frac{1}{2}})}^{(18 n - 1)} \times {(\sqrt{\frac{1}{2}})}^{2 n} \times {(\sqrt{\frac{4}{9}})}^{16 n} \times {(\sqrt{\frac{5}{12}})}^{n}$ ${= (\frac{2}{3})}^{16 n} \times {(\frac{\sqrt{5}}{4})}^{n} {\times (\frac{\sqrt{2}}{2})}^{27 n + 4} \times {(\frac{\sqrt{6}}{3})}^{9 n + 1} .$ $GAII (S P [n]) = \prod_{uvєE (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} = \prod_{u v є E_{3} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} \times \prod_{u v є E_{3}^{*} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} \times \prod_{u v є E_{6}^{*} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} \times \prod_{u v є E_{8}^{*} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} \times \prod_{u v є E_{9}^{*} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)} \times \prod_{u v є E_{7}^{*} (S P [n])} \frac{2 \sqrt{d (u) \times d (v)}}{d (u) + d (v)}$ $= {(\frac{2 \sqrt{2}}{3})}^{(2 n + 1)} \times {(\frac{\sqrt{3}}{2})}^{(9 n + 1)} \times {(\frac{2 \sqrt{4}}{5})}^{n} \times {(\frac{2 \sqrt{6}}{5})}^{(18 n - 1)} \times {(\frac{2 \sqrt{8}}{6})}^{2 n} \times {(\frac{2 \sqrt{12}}{7})}^{n}$ $= {(\frac{2 \sqrt{2}}{3})}^{2 n} \times {(\frac{16 \sqrt{3}}{35})}^{n} {\times (\frac{2 \sqrt{6}}{5})}^{18 n - 1} {\times (\frac{\sqrt{3}}{2})}^{9 n + 1} \times {(\frac{2 \sqrt{6}}{3})}^{2 n + 1} .$
5. The equations under Theorem 3 have been corrected as below: ${HII (S P [n]) = (\frac{2}{63})}^{n} \times {(\frac{1}{3})}^{16 n} \times {(\frac{2}{5})}^{19 n - 1} \times {(\frac{1}{2})}^{14 n + 5} \times {(\frac{2}{3})}^{2 n + 1}$ ${AZII (S P [n]) = (\frac{9}{4})}^{48 n} \times {(\frac{262144}{125})}^{n} \times {(\frac{3}{2})}^{27 n + 3} \times 8^{25 n + 4} .$
6. The equations in page 9 & 10, have been corrected as below: $HII (S P [n]) = \prod_{uvєE (S P [n])} \frac{2}{d (u) + d (v)} = \prod_{u v є E_{3} (S P [n])} \frac{2}{d (u) + d (v)} \times \prod_{u v є E_{3}^{*} (S P [n])} \frac{2}{d (u) + d (v)} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \frac{2}{d (u) + d (v)} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \frac{2}{d (u) + d (v)} \times \prod_{u v є E_{6}^{*} (S P [n])} \frac{2}{d (u) + d (v)} \times \prod_{u v є E_{8}^{*} (S P [n])} \frac{2}{d (u) + d (v)} \times \prod_{u v є E_{9}^{*} (S P [n])} \frac{2}{d (u) + d (v)} \times \prod_{u v є E_{7}^{*} (S P [n])} \frac{2}{d (u) + d (v)}$ $= \prod_{u v є E_{3} (S P [n])} \frac{2}{3} \times \prod_{u v є E_{3}^{*} (S P [n])} \frac{1}{2} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} \frac{2}{5} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} \frac{1}{2} \times \prod_{u v є E_{6}^{*} (S P [n])} \frac{2}{5} \times \prod_{u v є E_{8}^{*} (S P [n])} \frac{1}{3} \times \prod_{u v є E_{9}^{*} (S P [n])} \frac{1}{3} \times \prod_{u v є E_{7}^{*} (S P [n])} \frac{2}{7}$ $= {(\frac{2}{3})}^{(2 n + 1)} \times {(\frac{1}{2})}^{(9 n + 1)} \times {(\frac{2}{5})}^{n} \times {(\frac{1}{2})}^{(5 n + 4)} \times {(\frac{2}{5})}^{(18 n - 1)} \times {(\frac{1}{3})}^{2 n} \times {(\frac{1}{3})}^{16 n} \times {(\frac{2}{7})}^{n}$ ${= (\frac{2}{63})}^{n} \times {(\frac{1}{3})}^{16 n} \times {(\frac{2}{5})}^{19 n - 1} \times {(\frac{1}{2})}^{14 n + 5} \times {(\frac{2}{3})}^{2 n + 1} .$ $AZII (S P [n]) = \prod_{uvєE (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} = \prod_{u v є E_{3} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} \times \prod_{u v є E_{3}^{*} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} \times \prod_{u v є E_{6}^{*} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} \times \prod_{u v є E_{8}^{*} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} \times \prod_{u v є E_{9}^{*} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3} \times \prod_{u v є E_{7}^{*} (S P [n])} {(\frac{d (u) \times d (v)}{d (u) + d (v) - 2})}^{3}$ $= \prod_{u v є E_{3} (S P [n])} {(2)}^{3} \times \prod_{u v є E_{3}^{*} (S P [n])} {(\frac{3}{2})}^{3} \times \prod_{u v є E_{5} \cap E_{4}^{*} (S P [n])} {(\frac{4}{3})}^{3} \times \prod_{u v є E_{4} \cap E_{4}^{*} (S P [n])} {(2)}^{3} \times \prod_{u v є E_{6}^{*} (S P [n])} {(2)}^{3} \times \prod_{u v є E_{8}^{*} (S P [n])} {(2)}^{3} \times \prod_{u v є E_{9}^{*} (S P [n])} {(\frac{9}{4})}^{3} \times \prod_{u v є E_{7}^{*} (S P [n])} {(\frac{12}{5})}^{3}$ $= {(2)}^{3 (2 n + 1)} \times {(\frac{3}{2})}^{3 (9 n + 1)} \times {(\frac{4}{3})}^{3 n} \times {(2)}^{3 (5 n + 4)} \times {(2)}^{3 (18 n - 1)} \times {(2)}^{6 n} \times {(\frac{9}{4})}^{48 n} \times {(\frac{12}{5})}^{3 n}$ ${= (\frac{9}{4})}^{48 n} \times {(\frac{262144}{125})}^{n} \times {(\frac{3}{2})}^{27 n + 3} \times 8^{25 n + 4} .$
7. The table 1 was corrected as below:

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8. The table 2 was corrected as below:

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9. The table 3 was corrected as below:

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