Article ID: MTJPAM-D-23-00030

Title: Topological indices of some operations in cycle graphs related to EV and VE degrees


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00030; Volume 6 / Issue 1 / Year 2024, Pages 1-11

Document Type: Research Paper

Author(s): Deepasree Sasi Kumar a , Ranjini Poojakulangara Shankarawarrier b , Veerabhadraiah Lokesha c , Marannagari Phani Raju d

aAssistant Professor, Department of Mathematics, Acharya Institute of Technology, Bangalore-560107, Karnataka, India

bDepartment of Mathematics,Don Bosco Institute Of Technology, Kumbalagudu, Bangaluru-56, Karnataka, India

cDOS in Mathematics, Vijyanagara Sri Krishnadevaraya University, Ballari-583105, India

dPrincipal, Maharshi College of Education, Bengaluru-5, India

Received: 2 October 2023, Accepted: 26 December 2023, Published: 2 February 2024

Corresponding Author: Veerabhadraiah Lokesha (Email address: v.lokesha@gmail.com)

Full Text: PDF

Abstract

Topological indices are numerical variables through which we can derive a relationship between molecular structure of a compound and its physical or biological properties. First step of this process is to represent the molecular structure of the compound as a mathematical graph and then derive degree or distance based topological indices. There are many topological indices derived so far in chemical graph theory and many of them have established a strong relationship with properties of some compounds. This article gives estimation and comparison of some of such indices for graphs derived from simple cycle graphs through graph operations such as corona product, single edge connected graph and rooted product graph. Indices are based on VE and EV degree, which are recently added to the chemical graph theory.

Keywords: VE–EV degree, corona product, single edge connected graph, rooted product graph

References:
  1. N. Ananda, P. S. Ranjini, V. Lokesha and S. A. Wazzan, Subdivision and semitotal point graphs of Archimedean lattices on some toplogical indices, Proc. Jangjeon Math. Soc. 22 (4), 583–592, 2019; DOI: 10.17777/pjms2019.22.4.583.
  2. J. C. Bermond and C. Thomassen, Cycles in digraphs– a survey, J. Graph Theory 5 (1), 1–43, 1981; DOI:10.1002/jgt.3190050102.
  3. D. Bonchev, Chemical graph theory: Introduction and fundamentals, CRC Press, Boca Raton, 1991.
  4. J. A. Bondy and V. Chvatal, A method in graph theory, Discrete Math. 15 (2), 111–135, 1976; https://doi.org/10.1016/0012-365X(76)90078-9.
  5. M. Chellali, T. W. Haynes, S. T. Hedetniemi and T. M. Lewis, On ve-degrees and ev-degrees in graphs, Discrete Math. 340 (2), 31–38, 2017; https://doi.org/10.1016/j.disc.2016.07.008
  6. F. Harary, Graph theory reading, MA: Addison-Wesley, 1994.
  7. M. Ibrahim, N. Zahra and M. K. Siddiqui, On VE-degree and EV-degree based Topological indices for the series of Benzenoid graps, Polycycl. Aromat. Compd. 42 (7), 4726–4735, 2022; https://doi.org/10.1080/10406638.2021.1926294.
  8. D. S. Kumar and P. S. Ranjini, Zagreb indices of link graphs related to carbon nanotube and fullerene, Int. J. Health Sci. 6 (S8), 5671–5685, 2022; DOI: 10.53730/ijhs.v6nS8.13565.
  9. V. Lokesha, S. Jain, A. S. Cevik and I. N. Cangul, New results on the F-index of graphs based on a corona type products of graphs, Proc. Jangjeon Math. Soc. 23 (2), 141–148, 2020.
  10. A. Mahboob, D. Alrowili, S. Mahboob Alam, R. Ali, M. W. Rasheed and I. Siddique, Topological attributes of silicon carbide SiC4 − II[i, j] based on VE-degree and EV-degree, J. Chem. 2022, 2022; Article ID: 3188993, DOI:10.1155/2022/3188993.
  11. N. Malekmohammedi and A. R. Ashrafib, Caley graphs under graph operations II, Khayyam J. Math. 1 (2), 151–163, 2015.
  12. K. G. Mirajkar, A. Morajkar and H. H. Budihal, QSPR analysis of some chemical structures using KCD indices, AIP Conf. Proc. 2385, 030002-1–030002-4, 2022; DOI: 10.1063/5.0070746.
  13. P. G. Sheeja, P. S. Ranjini, V. Lokesha and A. S. Cevik, Computation of the SK Index over different corona products of graphs, Palest. J. Math. 10 (1), 8–16, 2021.
  14. B. S. Swetha, V. Lokesha and P. S. Ranjini, On the harmonic index of graph operations, Trans. Comb. 4 (4), 5–14, 2015.
  15. Z. Yarahmadia and A. R. Ashrafi, The Szeged, vertex PI, first and second Zagreb indices of corona product of graphs, Filomat 26 (3), 467–472, 2012; DOI:10.2298/FIL1203467Y.
  16. R. A. Zhong, A. Rauf, M. Naeem, J. Rahman and A. Aslam, Quantitative structure-property relationships (QSPR) of valency based topological indices with COVID-19 drugs and application, Arab. J. Chem. 14 (7), 2021; Article ID: 103240, DOI: 10.1016/j.arabjc.2021.103240.

Cite this article

How to cite this article: D. S. Kumar, R. P. Shankarawarrier, V. Lokesha and M. P. Raju, Topological indices of some operations in cycle graphs related to EV and VE degrees, Montes Taurus J. Pure Appl. Math. 6 (1), 1-11, 2024; Article ID: MTJPAM-D-23-00030.