Original Research Article

Article volume = 2024 and issue = 2

Pages: 234–247

Article publication Date: February 21, 2025

You can download PDF file of the article here: Download

Visited 41 times and downloaded 25 times

On first closed neighborhood Zagreb index of graph

B. Basavanagoud(a), Chetana S. Gali(b), and B. Bhuvana(b)

(a) Department of Mathematics, Karnatak University, Dharwad-580003, Karnataka, India.

(b) Department of Mathematics, Davangere University, Davangere-577007, Karnataka, India.

Abstract:

Topological indices are widely employed in the determination of the correlation between the physico-chemical properties of nanostructures. The development of novel nanostructures has important implications for the food science, electronics, pharmaceutical, medical, communication, and information sectors among others. In this paper, we introduce a new topological index called the first closed neighborhood Zagreb index and it exhibits good correlation with acentric factor of an octane isomers. We compute the formula for first closed neighborhood Zagreb index for some standard classes of graphs and investigate their mathematical properties. Further, we derive the expression for first closed neighborhood Zagreb index of $TUC_4C_8 (R) [p, q]$ nanostructures as well as subdivision graph and the line graph of the subdivision graph of $TUC_4C_8 (R) [p, q]$ nanostructures.

Keywords:

First closed neighborhood Zagreb index, Nanostructures, Subdivision graph, Line graph.

References:
  • [1] C. Adiga, A. Bayad, I. Gutman and S. A. Srinivas, The minimum covering energy of a digraph, Kragujevac J. Sci., 34 (2012),34–56. 3.3
  • [2] B. Basavanagoud, A. P. Barangi and S. M. Hosamani, First neighbourhood Zagreb index of some nanostructures, Proceedings of IAM., 7 (2018), 178–193. 1
  • [3] B. Basavanagoud, C. S. Gali, A note on certain topological indices of the derived graphs of subdivision graphs, TWMS J. App. Eng. Math., 1 (2020),208–219. 3.6
  • [4] Bondy, J.R.Murty, U.S.R. Graph theory, 1st ed.; Springer; New york; USA, (2008). 1
  • [5] B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem., 53 (2015),1184–1190. 1
  • [6] J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin., (2017). 3.4, 3.5, 3.7, 3.8, 3.9
  • [7] I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), 351–361. 1
  • [8] I. Gutman, N. Trinajsti´c, Graph theory and molecular orbitals, Total π−electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535–538. 1
  • [9] F. Harary, Graph Theory, Addison-Wesley Reading, Mass (1969). 1, 3.1, 3.2
  • [10] M. Karelson, Molecular Descriptors in QSAR/QSPR, New York, USA: Wiley-Interscience, (2000). 1
  • [11] MinatiKuanar, Saroj K Kuanar, Bijay K Mishra, and I. Gutman, Correlation of line graph parameters with physicochemical properties of octane isomers, Indian J. Chem., 38 (1999),525–528. 2
  • [12] Nadeem M. F, Zafar S and Zahid Z, On certain topological indices of the line graph of subdivision graphs, Appl. Math. Comput., 271 (2015),790–794. 5
  • [13] R Core Team. R, A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, (2016). URL https://www.R-project.org/. 2
  • [14] Su G and Xu L, Topological indices of the line graph of subdivision graphs and their Schur-bounds, Appl. Math. Comput., 253 (2015), 395–401. 5
  • [15] R. Todeschini, V. Consonni, Handbook of Molecul ar Descriptors, Wiley-VCH, Weinheim, (2000). 1
Cite this article as:
  • B. Basavanagoud, Chetana S. Gali, and B. Bhuvana, On first closed neighborhood Zagreb index of graph, Communications in Combinatorics, Cryptography & Computer Science, 2024(2), PP.234–247, 2025
  • Export citation to BibTeX