Study of generalized networks using graph theory

Year 2021, , 1491 - 1499, 15.10.2021

Tomas Vetrik

https://doi.org/10.15672/hujms.823694

Abstract

We study eccentricity-based indices such as Zagreb eccentricity indices, general eccentricity index and total eccentricity index. We present exact values of eccentricity-based indices of generalized networks related to binary and $m$-ary trees, where $m \ge 2$.

Keywords

graph theory, eccentricity-based index, network

References

• [1] F. Asif, Z. Zahid, S. Zafar, M.R. Farahani and W. Gao, On topological properties of some convex polytopes by using line operator on their subdivisions, Hacet. J. Math. Stat. 49 (1), 136–146, 2020.
• [2] R. Farooq and M.A. Malik, On some eccentricity based topological indices of nanostar dendrimers, Optoelectronics and Advanced Materials, Rapid Communications 9 (5- 6), 842–849, 2015.
• [3] W. Gao, H. Wu, M.K. Siddiqui and A.Q. Baig, Study of biological networks using graph theory, Saudi J. Biol. Sci. 25 (6), 1212–1219, 2018.
• [4] M. Ghorbani and M.A. Hosseinzade, A new version of Zagreb indices, Filomat 26 (1), 93–100, 2012.
• [5] M. Imran, M.A. Iqbal, Y. Liu, A.Q. Baig, W. Khalid and M.A. Zaighum, Computing eccentricity-based topological indices of 2-power interconnection networks, J. Chem. 2020, 3794592, 2020.
• [6] M.K. Siddiqui, M. Imran and M. Saeed, Topological properties of face-centred cubic lattice, Hacet. J. Math. Stat. 49 (1), 195–207, 2020.
• [7] D. Vukičević and A. Graovac, Note on the comparison of the first and second nor- malized Zagreb eccentricity indices, Acta Chim. Slov. 57 (3), 524–528, 2010.