Journal of Chemistry
Volume 2017 (2017), Article ID 6593090, 2 pages
https://doi.org/10.1155/2017/6593090

Letter to the Editor

Comment on “Topological Indices Study of Molecular Structure in Anticancer Drugs”

Akbar Ali

Department of Mathematics, University of Management and Technology, Sialkot, Pakistan

Correspondence should be addressed to Akbar Ali; akbarali.maths@gmail.com

Received 12 November 2016; Accepted 22 June 2017; Published 16 October 2017

Academic Editor: José L. Arias Mediano

Copyright © 2017 Akbar Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The formulae, reported in [1], for calculating some topological indices and polynomials of a specific molecular graph, can also be obtained from the general expressions which are derived from the graph quantities, calculated in the paper [2].

A topological index is said to be bond incident degree index (BID index, for short [3]) if it has the form of (1), given as follows. The BID index of a graph is defined [4, 5] as

where is a nonnegative real valued function depending on and such that and is the number of edges in the graph connecting the vertices of degrees and . Evidently, . Undefined notations and terminologies can be found in [1–5]. The BID polynomial of a graph can be defined as

Shetty et al. [2] calculated the graph quantities for the molecular graph (details about can be found in [1, 2]) as given as follows:

Substitution of these values in (1) and (2) gives formulae mentioned in the following theorem.

Theorem 1. The BID index and BID polynomial of the molecular graph are given as

Any formula for calculating a specific BID index or BID polynomial of the molecular graph , reported in [1], can also be obtained from (4) or (5), respectively, by taking suitable . Here, those two such formulae (namely, the first formula of Theorems  1 and 8) of [1] are rederived (given below in Corollary 2) which contained a typo/error.

The substitutions and in (1) give general sum-connectivity index and natural logarithm of the multiplicative sum Zagreb index , respectively, where is a nonzero real number and ln denotes the natural logarithm. Hence, the formulae given in the following corollary follow from (4).

Corollary 2 (see [1]). The general sum-connectivity index and multiplicative sum Zagreb index of the molecular graph are given as

Remark 3. The formula established in Theorem of [1] also contains a typo/error: the second last term of the aforementioned formula should be instead of .

Conflicts of Interest

The author declares that they have no conflicts of interest.

Acknowledgments

The author would like to thank Professor Wei Gao for his valuable comments on the letter.

References

W. Gao, W. F. Wang, and M. R. Farahani, “Topological indices study of molecular structure in anticancer drugs,” Journal of Chemistry, vol. 2016, Article ID 3216327, 8 pages, 2016.

B. S. Shetty, V. Lokesha, P. S. Ranjini, and K. C. Das, “Computing some topological indices of smart polymer,” Digest Journal of Nanomaterials and Biostructures, vol. 7, no. 3, pp. 1097–1102, 2012.

A. Ali, Z. Raza, and A. A. Bhatti, “Bond incident degree (BID) indices of polyomino chains: a unified approach,” Applied Mathematics and Computation, vol. 287-288, pp. 28–37, 2016.

B. Hollas, “The covariance of topological indices that depend on the degree of a vertex,” MATCH - Communications in Mathematical and in Computer Chemistry, vol. 54, no. 1, pp. 177–187, 2005.

D. Vukičević and M. Gašperov, “Bond additive modeling 1. adriatic indices,” Croatica Chemica Acta, vol. 83, pp. 243–260, 2010.