Volume 15, Issue 1 (4-2020)                   IJMSI 2020, 15(1): 1-13 | Back to browse issues page


XML Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Susanti Y, Puspitasari Y I, Khotimah H. On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs. IJMSI. 2020; 15 (1) :1-13
URL: http://ijmsi.ir/article-1-1121-en.html
Abstract:  
Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength of graph G and denoted by tes(G). In this paper, we determine the exact value of total edge irregularity strength for staircase graphs, double staircase graphs and mirror-staircase graphs.
Type of Study: Research paper | Subject: Special

References
1. [1] Ahmad, A., On the total edge irregularity strength of zigzag graphs, Australasian Journal of Combinatorics, Volume 54, Pages 141-149 (2012).
2. [2] Bau{c}a, M., Jendrol, S., Miller, M., Ryan, J. On irregular total labeling. Discrete Math, 307, 1378-1388 (2007). [DOI:10.1016/j.disc.2005.11.075]
3. [3] Chartrand, G., Jacobson, M.S., Lehel, J., Oellermann, O.R., Ruiz, S., Saba, F., Irregular networks, Congr. Numer. 64 pp. 355-374, (1988).
4. [4] Gallian, J.A. A dynamic survey of graph labeling, The Electronic Journal of Combinatorics,18, 247-252 (2015).
5. [5] Ivanco, J., Jendrol, S., The total edge irregularity strength of trees, Discuss. Math. Graph Theory, 26 pp. 449-456 (2006). [DOI:10.7151/dmgt.1337]
6. [6] Jendrol, S., Miskuf, J., Sotak, R., Total edge irregularity strength of complete graphs and complete bipartite graphs, Discrete Mathematics, Volume 310, Issue 3, Pages 400-407 (2010). [DOI:10.1016/j.disc.2009.03.006]
7. [7] Putra, R.W., Susanti, Y., On total edge irregularity strength of centralized uniform theta graphs, AKCE International Journal of Graphs and Combinatorics, volume 15 issue 1 page 7-13. (2018). [DOI:10.1016/j.akcej.2018.02.002]
8. [8] Putra, R.W., Susanti, Y., The total edge irregularity strength of uniform theta graphs, IOPScience Journal of Physics: Conference Series, 2018 J. Phys.: Conf. Ser. 1097 012069 (2018). [DOI:10.1088/1742-6596/1097/1/012069]
9. [9] Ratnasari L., Susanti, Y., Total edge irregularity strength of ladder related graphs, Asian-European Journal of Mathematics, doi:10.1142/S1793557120500722. [DOI:10.1142/S1793557120500722]
10. [10] L. Ratnasari, S. Wahyuni, Y. Susanti, D. Junia Eksi Palupi and B. Surodjo, Total edge irregularity strength of arithmetic book graphs, Journal of Physics: Conference Series 1306(1), 012032 (2019). [DOI:10.1088/1742-6596/1306/1/012032]
11. [11] Solairaju, A., Arockiasamy, A. M. Graceful mirror-staircase graphs, Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 49, 2433 - 2441 (2010).
12. [12] Wallis, W.D. Magic graphs. Boston: Birkhauser (2011).

Add your comments about this article : Your username or Email:
CAPTCHA

© 2020 All Rights Reserved | Iranian Journal of Mathematical Sciences and Informatics

Designed & Developed by : Yektaweb