TOTAL EDGE AND VERTEX IRREGULAR STRENGTH OF TWITTER NETWORK

  • Edy Saputra Rusdi Information Systems Study Program, FMIPA, Hasanuddin University
  • Nur Hilal A. Syahrir Actuarial Science Study Program, FMIPA, Hasanuddin University
DOI: https://doi.org/10.30598/barekengvol16iss1pp091-098
Keywords: the total edge irregularity strength, twitter network, the total vertex irregularity strength

Abstract

Twitter data can be converted into a graph where users can represent the vertices. Then the edges can be represented as relationships between users. This research focused on determining the total edge irregularity strength (tes) and the total vertices irregularity strength (tvs) of the Twitter network. The value could be determined by finding the greatest lower bound and the smallest upper bound. The lower bound was determined by using the properties, characteristics of the Twitter network graph along with the supporting theorems from previous studies, while the upper bound is determined through the construction of the total irregular labeling function on the Twitter network. The results in this study are the tes(TW)=18 and tvs(TW)=16.

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References

G. Chartrand and P. Zhang, Introduction to Graph Theory. Boston: Mc Graw-Hill Press, 2004.

M. Bača, S. Jendrol’, M. Miller, and J. Ryan, “On irregular total labellings,” Discrete Math., vol. 307, no. 11–12, pp. 1378–1388, 2007, doi: 10.1016/j.disc.2005.11.075.

J. A. Gallian, “A dynamic survey of graph labeling,” Electron. J. Comb., vol. 1, no. DynamicSurveys, 2018.

M. Bača, Z. Kimáková, M. Lascsáková, and A. Semaničová-Feňovčíková, “The Irregularity and Modular Irregularity Strength of Fan Graphs,” Symmetry (Basel)., vol. 13, no. 4, 2021, doi: 10.3390/sym13040605.

M. Bača, M. Imran, and A. Semaničová-Feňovčíková, “Irregularity and Modular Irregularity Strength of Wheels,” Mathematics, vol. 9, no. 21, 2021, doi: 10.3390/math9212710.

Slamin, “On distance irregular labelling of graphs,” Far East J. Math. Sci., vol. 102, no. 5, pp. 919–932, 2017, doi: 10.17654/MS102050919.

D. Indriati, Widodo, I. E. Wijayanti, K. A. Sugeng, and M. Bača, “On Total Edge Irregularity Strength of Generalized Web Graphs and Related Graphs,” Math. Comput. Sci., vol. 9, no. 2, pp. 161–167, 2015, doi: 10.1007/s11786-015-0221-5.

I. Rajasingh, B. Rajan, and S. Teresa Arockiamary, “Total Edge Irregularity Strength of Butterfly Networks,” Int. J. Comput. Appl., vol. 49, no. 3, pp. 21–22, 2012.

Nurdin, “Total irregular labeling of butterfly network on level two,” AIP Conf. Proc., vol. 1867, no. August, 2017, doi: 10.1063/1.4994470.

Nurdin, E. T. Baskoro, A. N. M. Salman, and N. N. Gaos, “On the total vertex irregularity strength of trees,” Discrete Math., vol. 310, no. 21, pp. 3043–3048, 2010, doi: 10.1016/j.disc.2010.06.041.

. Nurdin, M. Zakir, and Firman, “Vertex-irregular labeling and vertex-irregular total labeling on caterpillar graph,” Int. J. Appl. Math. Stat., vol. 40, pp. 99–105, Jan. 2013.

N. Hinding, H. K. Kim, N. Sunusi, and R. Mise, “On Total Vertex Irregularity Strength of Hexagonal Cluster Graphs,” Int. J. Math. Math. Sci., vol. 2021, 2021, doi: 10.1155/2021/2743858.

E. Saputra, N. Hinding, and S. Amir, “Total Irregular Labelling Of Butterfly and Beneš Network 5-Dimension,” J. Mat. Stat. dan Komputasi, vol. 17, no. 1, pp. 61–70, 2020, doi: 10.20956/jmsk.v17i1.10909.

M. Imran, A. Ahmad, M. K. Siddiqui, and T. Mehmood, “Total vertex irregularity strength of generalized prism graphs,” J. Discret. Math. Sci. Cryptogr., 2021, doi: 10.1080/09720529.2020.1848103.

M. I. Tilukay, P. D. M. Taihuttu, A. N. M. Salman, F. Y. Rumlawang, and Z. A. Leleury, “Complete bipartite graph is a totally irregular total graph,” Electron. J. Graph Theory Appl., vol. 9, no. 2, p. 387, 2021, doi: 10.5614/ejgta.2021.9.2.11.

G. K. Nandini, R. S. Rajan, A. A. Shantrinal, T. M. Rajalaxmi, I. Rajasingh, and K. Balasubramanian, “Topological and thermodynamic entropy measures for covid-19 pandemic through graph theory,” Symmetry (Basel)., vol. 12, no. 12, pp. 1–29, 2020, doi: 10.3390/sym12121992.

Published
2022-03-21
How to Cite
[1]
E. Rusdi and N. A. Syahrir, “TOTAL EDGE AND VERTEX IRREGULAR STRENGTH OF TWITTER NETWORK”, BAREKENG: J. Math. & App., vol. 16, no. 1, pp. 091-098, Mar. 2022.
Issue
Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Section
Articles

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