Original Research Article

Article volume = 2021 and issue = 2

Pages: 163–171

Article publication Date: November, 1, 2021

You can download PDF file of the article here: Download

Visited 377 times and downloaded 208 times

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
  • Export citation to BibTeX