Original Research Article

Article volume = 2021 and issue = 2

Pages: 163–171

Article publication Date: November, 1, 2021

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# Mostar Index of Conical and Generalized Gear Graph

#### P. Kandan(a), S. Subramanian(b)

(a)Assistant Professor, PG and Research Department of Mathematics Government Arts College, Chidambaram 608102, India.

(b)Department of Mathematics, Annamalai University Annamalai Nagar 608002, India

##### Abstract:

In theoretical chemistry, topological index play a significant role. Bond-additive index have been utilized more extensively than other topological indices that quantify graph peripherality. In this study, we compute the exact formula of one of the recently introduced bond-additive topological index called Mostar Index to the conical graph C(ℓ, k). Using the result obtained here, we have corrected the result obtained by Colako ˇ glu Havare. Moreover we obtained the Mostar index to the new graph called generalized gear graph C ∗ (ℓ, 2k).

##### Keywords:

Conical graph, Gear graph, Mostar index.

##### References:

- [1] T. Al-Fozan, P. Manuel, I. Rajasingh, and R. Sundara Rajan Computing Szeged Index of Certain Nanosheets Using Partition Technique, arXiv:2103.04018v1 [math.CO](2021) 1
- [2] M. Arockiaraj, J. Clement, N. Tratnik Mostar indices of carbon nanostructures and circumscribed donut benzenoid systems , Quntam chemistry https://doi.org/10.1002/qua.26043 (2019) 1
- [3] A.Q. Alameri, M.M. Shubatah and M.S. Alshafi, Hyper Zageb Indices and Redfined Zagreb Indices of Conical Graphs, Advance in Mathematics: Scientific Journal, 9 (2020) 3643-3652. 1
- [4] A. Alia T.Došlićb, Mostar index: Results and perspectives, Applied Mathematics and Computation, 404, (2021), 126245 1
- [5] A. Ayache, A. Alumeri, A. Ghallb,and A. Modabish, Wiener Polynomial and Wiener index of Conical Graphs, sylwan., 3 (2020) 164. 1
- [6] ¨O. Colako ˘ glu Havare, Mostar Index (Mo) and Edge (Mo) Index of some Cycle Related Graphs Romanian journal of Mathematics and computer Science, 10 (2020) 53-66. 1, 2.1, 2.2
- [7] ¨O. Colako ˘ glu Havare, Mostar Index of bridge graphs TWMS J.App.and Eng. Math.,11 (2021) 587-697. 1
- [8] A. Dobrynin, The Szeged and Wiener indices of line graphs, MATCH Commun. Math. Com-put. Chem., 79 (2018) 743–756. 1
- [9] T.Doˇsli ´c, Mostar index, J. Math. Chem. 56 (2018) 2995–3013. 1
- [10] T.Doˇsili ´c, I. Martinjak, R. Skrekovski, S. Tipuric, S. Spuzevic and I. Zubac Mostar index journal of Mathematical Chemistry, 56 (2018) 2995-3013. 1
- [11] I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N.Y. 27 (1994) 9–15. 1
- [12] W. Gao, L. Shi Hyper-Wiener Index of gear and gear wheel related graph, In J Chem Stud., 2 (2015) 52-58. 2.2
- [13] W. Gao and W. Wang, Second atom-bond connectivity index of special chemical molecular structures, Journal of Chemistry, 2014 (2014) Article ID 906254. 2.2
- [14] J. Geneson, S. Tsai, Peripherality in networks: theory and applications,arXiv:2110.04464v1 [math.CO] 9 Oct 2021. 1
- [15] N. Ghanbari, S. Alikhani, Mostar index and edge Mostar index of polymers,Computational and Applied Mathematics (2021) 40:260. 1
- [16] A. Ghalavand, A. R. Ashrafi and M. Hakimi-Nezhaad On Mostar and Edge Mostar Indices of Graphs, Hindawi Journal of Mathematics, 2021, Article ID 6651220, 14 . 1
- [17] G. Indulal, L. Alex1, I. Gutman On graphs preserving PI index upon edge removal , Journal of Mathematical Chemistry, 59, (2021), 1603–1609. 1
- [18] M. Knor, R. Skrekovski, A. Tepeh, Mathematical Aspects of Wiener Index, Ars. math. contemp. 11 (2016) 327-352. 1
- [19] P. Kandan, S. Subramanian, On Mostar Index of Graph, Adv. Math.: Sci. J., 10 (2021) 2115-2126. 1, 2.2
- [20] P. Kandan, S. Subramanian and P. Rajesh, Weighted Mostar indices of certain graph, Adv. Math.: Sci. J. 10 (2021), no.9, 3093–3111 1, 2.2
- [21] P. Kandan, S. Subramanian, Computation of weighted PIand Szeged indices of conical graph,(Accepted: IJONS) 1, 2.2
- [22] P. Kandan, S. Subramanian, Some Bond-Additive Indices of Graphs,(Accepted : ICDM2021) 1, 2.2
- [23] H. Liu, On the Maximal Mostar Index of Tree-Type Phenylenes , (2021), Polycyclic aromatic compounds, https://doi.org/10.1080/10406638.2021.1873151. 1
- [24] P. Shiladhar, A.M. Naji and N.D. Soner Leaf Zagred indices of some wheel Related Graphs Journal of Computer and Mathematical Science, 9 (2018) 221-231. 2.2
- [25] N. Tranik Computing the Mostar index in networks with application to molecular graphs, Iranian J. math. chem. 12 (2021) 1-18. 1
- [26] N. Tranik Computing weighted Szeged and PI indices from quotient graphs, Quntam Chemistry, DOI: 10.1002/qua.26006. 1

##### Cite this article as:

- P. Kandan, S. Subramanian, Mostar Index of Conical and Generalized Gear Graph, Communications in Combinatorics, Cryptography & Computer Science, 2021(2), PP.163–171, 2021
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