آمار
| تعداد نشریات | 5 |
| تعداد شمارهها | 116 |
| تعداد مقالات | 1,359 |
| تعداد مشاهده مقاله | 1,365,214 |
| تعداد دریافت فایل اصل مقاله | 1,322,529 |
Exploring the Precise Edge Irregularity Strength of Generalized Arithmetic and Geometric Staircase Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 10، شماره 4، اسفند 2025، صفحه 825-835 اصل مقاله (971.99 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28992.1804 | ||
| نویسندگان | ||
| Yeni Susanti* ؛ Muhammad Nurul Huda؛ Ramadhani Latief Firmansyah | ||
| Department of Mathematics, Universitas Gadjah Mada, Indonesia | ||
| چکیده | ||
| In the context of a finite undirected graph $\zeta$, an edge irregular labelling is defined as a labelling of its vertices with some labels in such a way that each edge has a unique weight, which is determined by the sum of the labels of its endpoints. The main objective of this study is to determine the smallest positive integer $n$ for which it is possible to assign a total edge irregular labelling to $\zeta$ with $n$ as the biggest label. This investigation focuses particularly on cases where $\zeta$ represents the generalized arithmetic and generalized geometric staircase graphs. Within this paper, the definition of generalized geometric staircase graph is proposed. Moreover, we not only establish the edge irregularity strength of these two kind of graphs but also present a method for creating the corresponding edge irregular labelling. | ||
| کلیدواژهها | ||
| irregular labeling؛ staircase graphs؛ total edge irregularity strength | ||
| مراجع | ||
|
[1] A. Ahmad, O.B.S. Al-Mushayt, and M. Bača, On edge irregularity strength of graphs, Appl. Math. Comput. 243 (2014), 607–610. https://doi.org/10.1016/j.amc.2014.06.028
[2] A. Ahmad, K.M. Awan, I. Javaid, and S. Slamin, Total vertex irregularity strength of wheel related graphs., Australas. J. Comb. 51 (2011), 147–156.
[3] A. Ahmad, S.S. Khan, S. Ahmad, M.F. Nadeem, and M.K. Siddiqui, Edge irregularity strength of categorical product of two paths, Ital. J. Pure Appl. Math. 45 (2021), 801–813.
[4] M. Bača, S. Jendrol’, M. Miller, and J. Ryan, On irregular total labellings, Discrete Math. 307 (2007), no. 11–12, 1378–1388. https://doi.org/10.1016/j.disc.2005.11.075
[5] M. Bača and M.K. Siddiqui, Total edge irregularity strength of generalized prism, Appl. Math. Comput. 235 (2014), 168–173. https://doi.org/10.1016/j.amc.2014.03.001
[6] G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz, and F. Saba, Irregular networks, Congr. Numer. 64 (1988), 197–210.
[7] J.A. Gallian, Graph labeling, Electron. J. Comb. 18 (2023), #DS6.
[8] N. Hinding, E.T. Baskoro, A.N.M. Salman, and N.N. Gaos, On the total vertex irregularity strength of trees, Discrete Math. 310 (2010), no. 21, 3043–3048. https://doi.org/10.1016/j.disc.2010.06.041
[9] M.N. Huda and Y. Susanti, Total edge irregular labeling for triangular grid graphs and related graphs, BAREKENG: J. Math. Appl. 17 (2023), no. 2, 0855–0866. https://doi.org/10.30598/barekengvol17iss2pp0855-0866
[10] J. Ivančo and S. Jendrol, Total edge irregularity strength of trees, Discuss. Math. Graph Theory 26 (2006), no. 3, 449–456.
[11] S. Jendrol’, J. Miškuf, and R. Soták, Total edge irregularity strength of complete graphs and complete bipartite graphs, Discrete Math. 310 (2010), no. 3, 400–407. https://doi.org/10.1016/j.disc.2009.03.006
[12] C. Jordán, M. Murillo-Arcila, and J.R. Torregrosa, The STEM methodology and graph theory: Some practical examples, Mathematics 9 (2021), no. 23, Article ID: 3110. https://doi.org/10.3390/math9233110
[13] R. Ramdani, A.N.M. Salman, and H. Assiyatun, On the total edge and vertex irregularity strength of some graphs obtained from star, J. Indones. Math. Soc. 25 (2019), no. 3, 314–324. https://doi.org/10.22342/jims.25.3.828.314-324
[14] R. Simanjuntak, S. Susilawati, and E.T. Baskoro, Total vertex irregularity strength for trees with many vertices of degree two., Electron. J. Graph Theory Appl. 8 (2020), no. 2, 415–421. https://dx.doi.org/10.5614/ejgta.2020.8.2.17
[15] Y. Susanti, Y.I. Puspitasari, and H. Khotimah, On total edge irregularity strength of staircase graphs and related graphs, Iran. J. Math. Sci. Inform. 15 (2020), no. 1, 1–13. http://dx.doi.org/10.29252/ijmsi.15.1.1
[16] Y. Susanti, S. Wahyuni, A. Sutjijana, S. Sutopo, and I. Ernanto, Generalized arithmetic staircase graphs and their total edge irregularity strengths, Symmetry 14 (2022), no. 9, Article ID: 1853. https://doi.org/10.3390/sym14091853
[17] S. Susilawati, E.T. Baskoro, R. Simanjuntak, and J. Ryan, On the vertex irregular total labeling for subdivision of trees, Australas. J. Comb. 71 (2018), no. 2, 293–302.
[18] I. Tarawneh, R. Hasni, and A. Ahmad, On the edge irregularity strength of corona product of graphs with paths, Appl. Math. E-Notes 16 (2016), 80–87.
[19] I. Tarawneh, R. Hasni, and A. Ahmad, On the edge irregularity strength of grid graphs, AKCE Int. J. Graphs Comb. 17 (2020), no. 1, 414–418. https://doi.org/10.1016/j.akcej.2018.06.011
[20] I. Tarawneh, R. Hasni, A. Ahmad, and M.A. Asim, On the edge irregularity strength for some classes of plane graphs, AIMS Math. 6 (2021), no. 3, 2724–2731. https://doi.org/10.3934/math.2021166
[21] I. Tarawneh, R. Hasni, A. Ahmad, G.C. Lau, and S.M. Lee, On the edge irregularity strength of corona product of graphs with cycle, Discrete Math. Algorithms Appl. 12 (2020), no. 6, Article ID: 2050083. https://doi.org/10.1142/S1793830920500834
[22] I. Tarawneh, R. Hasni, M.K. Siddiqui, and M.A. Asim, On the edge irregularity strength of disjoint union of certain graphs, Ars Combin. 142 (2019), 239–249.
[23] F. Werner, Graph-theoretic problems and their new applications, Mathematics 8 (2020), no. 3, Article ID: 445. https://doi.org/10.3390/math8030445
[24] R.W.N. Wijaya, J. Ryan, and T. Kalinowski, Total edge irregularity strength of the cartesian product of bipartite graphs and paths, J. Indones. Math. Soc. 29 (2023), no. 2, 156–165. https://doi.org/10.22342/jims.29.2.1321.156-165 | ||
|
آمار تعداد مشاهده مقاله: 532 تعداد دریافت فایل اصل مقاله: 984 |
||