Total Absolute Difference Edge Irregularity Strength of Several Ladder-type Graphs

Faisal Susanto; Kristiana Wijaya

doi:10.37905/euler.v14i2.39334

Total Absolute Difference Edge Irregularity Strength of Several Ladder-type Graphs

Faisal Susanto, Kristiana Wijaya

Abstract

This paper studies edge irregular total absolute difference labeling for several classes of ladder-related graphs, namely triangular ladders, alternating triangulated ladders, and double triangulated ladders. By deriving coinciding lower and upper bounds, the precise values for the total absolute difference edge irregularity strength of these graphs are successfully established.

Keywords

Edge Irregular Total; Absolute Difference Labeling; Triangular Ladder; Alternating Triangulated Ladder; Double Triangulated Ladder

Full Text:

PDF

References

J. A. Gallian, “A dynamic survey of graph labeling,” Electronic Journal of Combinatorics, p. #DS6, 2025, doi: 10.37236/27.

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

M. R. Z. El Deen and G. M. Elmahdy, “Total edge irregularity strength and edge irregular reflexive labeling for calendula graph,” Italian Journal of Pure and Applied Mathematics, no. 49, pp. 722–753, 2023, Available: https://ijpam.uniud.it.

L. Ratnasari, S. Wahyuni, Y. Susanti, and D. J. Eksi Palupi, “Total edge irregularity strength of modified book graphs,” Southeast Asian Bulletin of Mathematics, vol. 47, no. 4, pp. 543–562, 2023, Available: http://www.seams-bull-math.ynu.edu.cn/archive.jsp.

A. Sudha and P. Jeyanthi, “Total edge irregularity strength of some graphs,” International Journal of Mathematical Analysis and Research, vol. 1, no. 2, pp. 16–20, 2025, doi: 10.64137/31082637/IJMARV1I2P103.

Nikita, S. Nurhayati, T. M. A. Januaviani, S. Musdalifah, I. Al Fajri, and Andri, “Total edge irregularity strength of graph L3 ⊙Nm,” Riemann: Research of Mathematics and Mathematics Education, vol. 7, no. 2, pp. 104–110, 2025, doi: 10.38114/reimann.v7i2.104.

H. Attiya, N. Ahmed, and F. Salama, “Total edge irregularity strength of star snake graphs,” European Journal of Pure and Applied Mathematics, vol. 18, no. 2, pp. 5673–5673, 2025, doi: 10.29020/nybg.ejpam.v18i2.5673.

H. Attiya, “Study on electromagnetic Feynman graph and its total edge irregularity strength,” Delta Journal of Science, vol. 50, no. 1, pp. 120–128, 2025, doi: 10.21608/djs.2025.372919.1210.

S. Pranata, V. H. Krisnawati, and D. Darmajid, “Total edge irregularity strength of cycle snake graphs,” CAUCHY: Jurnal Matematika Murni dan Aplikasi, vol. 11, no. 1, pp. 970–986, 2026, doi: 10.18860/cauchy.v11i1.41552.

E. Wulandari and Y. Susanti, “On total edge irregularity strength of arithmetic ladder graphs,” AIMS Mathematics, vol. 11, no. 4, pp. 10 175–10 190, 2026, doi: 10.3934/math.2026420.

M. Ramalakshmi and K. M. Kathiresan, “Total absolute difference edge irregularity strength of the graph,” Kragujevac Journal of Mathematics, vol. 46, no. 6, pp. 895–903, 2022, doi: 10.46793/KgJMat2206.895R.

A. Lourdusamy, F. J. Beaula, and F. Patrick, “Total absolute difference edge irregularity strength of Tptree graphs,” Proyecciones, vol. 42, no. 6, pp. 1597–1614, 2023, doi: 10.22199/issn.0717-6279-5411.

A. Lourdusamy and F. Joy Beaula, “Total absolute difference edge irregularity strength of some families of graphs,” TWMS Journal of Applied and Engineering Mathematics, vol. 13, no. 3, pp. 1005–1012, 2023, Available: https://jaem.isikun.edu.tr/web/images/articles/vol.13.no.3/17.pdf.

K. Shabbir, A. Raza, and L. Guran, “Computation of tades of some families of graphs,” Scientific Inquiry and Review, vol. 8, no. 4, pp. 80–92, 2024, doi: 10.32350/sir.84.04.

A. Lourdusamy and F. J. Beaula, “On tades of transformed tree and path related graphs,” Jordan Journal of Mathematics and Statistics, vol. 17, no. 1, pp. 129–143, 2024, doi: 0.47013/17.1.8.

A. Lourdusamy, F. Beaula, and F. Patrick, “On tades of disjoint union of some graphs,” Ars Combinatoria, vol. 157, pp. 89–94, 2023, doi: 10.61091/ars157-09.

DOI: https://doi.org/10.37905/euler.v14i2.39334