DOI QR코드

DOI QR Code

TOPOLOGICAL ANALYSIS OF SUPER-DYADIC GRAPHS

  • P. ANAGHA (Dept. of Mathematics, School of Advanced Sciences, Vellore Institute of Technology) ;
  • R. SELVAKUMAR (Dept. of Mathematics, School of Advanced Sciences, Vellore Institute of Technology)
  • Received : 2024.01.23
  • Accepted : 2024.11.14
  • Published : 2025.01.30

Abstract

For the topological analysis of complex networks having a super-dyadic nature, hypergraph representation is more convenient than graph representation in many cases. This paper presents new parameters that can be used to investigate the interactions between various network nodes. Based on this parameter, topological indices are defined and discussed. To construct a hypergraph with a highly modular structure, this paper introduces an inequality.

Keywords

References

  1. Sinan G. Aksoy, Cliff Joslyn, Carlos Ortiz Marrero, Brenda Praggastis and Emilie Purvine, Hypernetwork science via high-order hypergraph walks, EPJ Data Sci. 9 (2020), 16. https://doi.org/10.1140/epjds/s13688-020-00231-0.
  2. Alcalá-Corona, Sergio Antonio, Santiago Sandoval-Motta, Jesus Espinal-Enriquez and Enrique Hernandez-Lemus, Modularity in biological networks, Front. genet. 12 (2021), 701331. https://doi.org/10.3389/fgene.2021.701331.
  3. A. Puthanpurakkal and S. Ramachandran, Study on structural properties of brain networks based on independent set indices, Symmetry 15 (2023), 1032. https://doi.org/10.3390/sym15051032.
  4. Andre Ebling Brondani, Carla Silva Oliveira, Francisca Andrea Macedo França and Leonardo de Lima, Aα -Spectrum of a firefly graph, ENTCS 346 (2019), 209-219. https://doi.org/10.1016/j.entcs.2019.08.019.
  5. H.M. Awais, Muhammad Javaid and Akbar Ali, First general Zagreb index of generalized F-sum graphs, Discrete Dyn. Nat. Soc. 2020 (2020), Article ID 2954975. https://doi.org/10.1155/2020/2954975.
  6. S.G. Balogh, B. Kovács, and G. Palla, Maximally modular structure of growing hyperbolic networks, Commun. Phys. 6 (2023). https://doi.org/10.1038/s42005-023-01182-4.
  7. A. Bretto, Applications of hypergraph theory: a brief overview, In: Hypergraph Theory, Math. eng., Springer, Heidelberg, 2013. https://doi.org/10.1007/978-3-319-00080-0 7.
  8. Domingos M. Cardoso, Maria Aguieiras A. de Freitas, Enide Andrade Martins and Maŕıa Robbiano, Spectra of graphs obtained by a generalization of the join graph operation, Discrete Math. 313 (2013), 733–741. https://doi.org/10.1016/j.disc.2012.10.016.
  9. Wei Gao, Zahid Iqbal, Muhammad Ishaq, Rabia Sarfraz, Muhammad Aamir and Adnan Aslam, On eccentricity-based topological indices study of a class of porphyrin-cored dendrimers, Biomolecules 8 (2018), 71. https://doi.org/10.3390/biom8030071.
  10. F. Harary, Graph Theory, Narosa Publishing House, New Delhi, 2001.
  11. Syed Ajaz K. Kirmani, Parvez Ali and Faizul Azam, Topological indices and QSPR/QSAR analysis of some antiviral drugs being investigated for the treatment of COVID-19 patients, Int. J. Quantum Chem. 121 (2021), e26594. https://doi.org/10.1002/qua.26594.
  12. Robert Kooij, On generalized windmill graphs, Linear Algebra Appl. 565 (2019), 25-46. https://doi.org/10.1016/j.laa.2018.11.025.
  13. Li, Chenhui, George Baciu, and YunzheWang, Modulgraph: modularity-based visualization of massive graphs, In SIGGRAPH Asia 2015 Visualization in High Performance Computing, pp. 1-4, 2015. https://doi.org/10.1145/2818517.2818542.
  14. Xuhong Liao, Athanasios V. Vasilakos and Yong He, Small-world human brain networks: Perspectives and challenges, Neurosci Biobehav Rev. 77 (2017), 286-300. https://doi.org/10.1016/j.neubiorev.2017.03.018.
  15. Weichan Liu and Guiying Yan, Hypergraph incidence coloring, Discrete Math. 346 (2023), 113311. https://doi.org/10.1016/j.disc.2022.113311.
  16. M. M. Matejic, I. Z. Milovanovic and E. I. Milovanovic, Some inequalities for gen-eral sum-connectivity index, J. Appl. Math. and Informatics 38 (2020), 189-200. https://doi.org/10.14317/jami.2020.189.
  17. Newman, E.J. Mark, Modularity and community structure in networks, Proceedings of the national academy of sciences 103 (2006), 8577-8582. https://doi.org/10.1073/pnas.060160210.
  18. Saleh, Anwar, Sara Bazhear and Najat Muthana, Uphill Zagreb indices of some graph operations for certain graphs, J. Appl. Math. and Informatics 40 (2022), 959-977. https://doi.org/10.14317/jami.2022.959.
  19. Zehui Shao, Muhammad Kamran Siddiqui and Mehwish Hussain Muhammad, Computing Zagreb indices and Zagreb polynomials for symmetrical nanotubes, Symmetry 10 (2018), 244. https://doi.org/10.3390/syml0070244.
  20. G. H. Shirdel, H. Rezapour and A. M. Sayadi, The hyper-Zagreb index of graph operations, Iran. J. Math. Chem. 4 (2013), 213-220. https://doi.org/10.22052/ijmc.2013.5294.
  21. V. Voloshin, Introduction to Graph and Hypergraph Theory. Hauppauge, Nova Science, NY, 2009. ISBN: 1614701121, 9781614701125.
  22. Jian-Feng Zhong, Abdul Rauf, Muhammad Naeem, Jafer Rahman and Adnan Aslam, Quantitative structure-property relationships (QSPR) of valency-based topological an-dices with Covid-19 drugs and application, Arab. J. Chem. 14 (2021), 103240. https://doi.org/10.1016/j.arabjc.2021.103240.