Some Types of Irregular Labeling of Diamond Networks on Ten Vertices

Nurdin Hinding; Ali  Ahmad; Jusmawati Jusmawati

doi:10.20956/j.v18i2.17905

Authors

Nurdin Hinding Department of MathematicsFaculty of Mathematics and Natural SciencesHasanuddin University http://orcid.org/0000-0002-9894-061X
Ali Ahmad College of Computer Sciences and Information Technology, Jazan University
Jusmawati Jusmawati HASANUDDIN UNIVERSITY

DOI:

https://doi.org/10.20956/j.v18i2.17905

Keywords:

Diamond graph, irregular labeling, network

Abstract

There are three interesting parameters in irregular networks based on total labelling, i.e. the total vertex irregularity strength, the total edge irregularity strength, and the total irregularity strength of a graph. Besides that, there is a parameter based on edge labelling, i.e., the irregular labelling. In this paper, we determined the four parameters for diamond graph on eight vertices.

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References

Ahmad, Nurdin, and E. T. Baskoro, “On Total Irregularity Strength of Generalized Halin Graph”, Ars Combinatoria, vol. 122, pp. 319 – 332, 2015.

M. Aigner and E. Triesch, “Irregular assignments of trees and forests”, SIAM Journal Discrete Mathematics, vol. 3, pp. 439 – 449, 1990.

M. Bača, S. Jendrol, M. Miller, and J. Ryan, “On Irregular Total Labelling”. Discrete Mathematics, vol. 307, pp. 1378 – 1388, 2007.

G. Chartrand, M. S. Jacobson, J. Lehel, O. R. Oellermann, S. Ruiz, and F. Saba, “Irregular Networks”, Congressus Numerantium, vol. 64, pp. 197 – 210, 1988.

R. J. Faudree and J. Lehel, “Bound on the irregularity strength of regular graphs”, in Combinatorics, Colloq. Math. Soc. János Bolyai 52, North Holland, Amsterdam, pp. 247 – 256, 1987.

J.A. Gallian, Graph labeling, Electron. J. Combin. vol. 17, 2019. (Dynamic Survey DS#6).

Marzuki, A. N. M. Salman, and M. Miller, “On the Total Irregularity Strength of Cycle and Path”, Far East Journal of Mathematics and Science, vol. 8, no. 21, pp. – 21, 2013.

Nurdin, E.T.Baskoro, A.N.M.Salman, N.N.Gaos, “On the Total Vertex Irregularity Strength of Trees”, Discrete Mathematics, vol. 310, no. 21, pp. 3043 – 3048, 2010.

Nurdin, H,K.Kim, “Irregular Labeling on Transportation Network of Splitting graphs of stars”, Proceedings of the Jangjeon Mathematical Society, vol. 22, no. 1, pp. 103 – 108, 2019.

Nurdin, M.Zakir, Firman, Vertex-irregular labeling and vertex-irregular total labeling on caterpillar graph, “International Journal of Applied Mathematics and Statistics, vol. 40, no. 10, pp. 99-105, 2013.

R.Ramdani and A. N. M. Salman, “On The Total Irregularity Strength of Some Cartesian Product Graphs”, AKCE International Journal of Graphs and Combinatorics, vol. 10, no. 2, pp. 199 – 209, 2013.

J.Sedlàček, “Problem 27 in Theory Graphs and Its Applications”, Proceedings of the Symposiu Smolenice, pp. 163 – 167, 1963.

M.A.Shulhany and A. N. M. Salman, “Bilangan Terhubung Pelangi Graf Berlian”, Prosiding Seminar Nasional Matematika dan Pendidikan Matematika UMS, pp. 916 – 924, 2015. 11

M.K.Siddiqui, Nurdin, E.T.Baskoro, “Total edge irregularity strength of the disjoint union of helm graphs”, Journal of Mathematical and Fundamental Sciences, vol. 45, no. 2, pp. 163-171, 2013.

K.Wijaya and Slamin, “Total Vertex Irregular Labellings of Wheels, Fans, Suns, and Friendship Graphs”, Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 56, pp. 103 – 112, 2008.