TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Open Access Research Article

Edge reflexive irregularity strength of mk -graph of path graph 

, , *

* Corresponding author · click or hover a name for details

pp. 235–250Vol. 47Issue 1January 2026DOI: 10.47974/JIOS-1586XML
Received:
13 Sep 2023
Published Online:
03 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1586
Pages:
235–250

Abstract

In graph theory we define the total labeling, such that the edge labels and vertex labels are positive integers and even integers respectively and for different edges we have distinct weights, whereas the weight of an edge is the sum of labels of that edge and adjacent vertices, then labeling is referred as edge irregular reflexive total labeling. In this paper we calculated the exact values of reflexive edge irregularity strength for mk-graph of path graph mPn for k = 1 with n ≥ 3, m ≥ 4.

Keywords

Subject Classifications

05C7805C70

References

[1] A. Ahmad, M. Bača, Y. Bashir, and M. K. Siddiqui, “Total edge irregularity strength of strong product of two paths,” Ars Combinatoria, vol. 106, pp. 449-459 (2012).
[2] A. Ahmad, O. B. S. Al-Mushayt, and M. Baa, “On edge irregularity strength of graphs,” Applied Mathematics and Computation, vol. 243, pp. 607-610 (2014).
[3] M. Anholcer and C. Palmer, “Irregular labelings of circulant graphs,” Discrete Mathematics, vol. 312, no. 23, pp. 3461-3466 (2012).
[4] A. Ayache and A. Alameri, “Topological indices of the mk-graph,” Journal of the Association of Arab Universities for Basic and Applied Sciences, vol. 24, pp. 283-291 (2017).
[5] M. Bača and M. K. Siddiqui, “Total edge irregularity strength of generalized prism,” Applied Mathematics and Computation, vol. 235, pp. 168-173 (2014).
[6] M. Bača, M. Miller, and J. Ryan, “On irregular total labellings,” Discrete Mathematics, vol. 307, no. 11-12, pp. 1378-1388 (2007).
[7] G. Chartrand, M. S. Jacobson, J. Lehel, O. R. Oellermann, S. Ruiz, and F. Saba, “Irregular networks,” Congr. Numer., vol. 64, pp. 197-210, 250th (1988).
[8] S. W. Golomb, “How to number a graph,” in Graph Theory and Computing, pp. 23-37, Academic Press (1972).
[9] M. Imran, A. Ahmad, M. K. Siddiqui, and T. Mehmood, “Total vertex irregularity strength of generalized prism graphs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 6, pp. 1855-1865 (2022).
[10] J. Ivančo and S. Jendrol, “Total edge irregularity strength of trees,” Discussiones Mathematicae Graph Theory, vol. 26, no. 3, pp. 449-456 (2006).
[11] S. Jendrol’, J. Miškuf, and R. Sotk, “Total edge irregularity strength of complete graphs and complete bipartite graphs,” Discrete Mathematics, vol. 310, no. 3, pp. 400-407 (2010).
[12] C. C. Marzuki, A. N. M. Salman, and M. Miller, “On the total irregularity strength of cycles and paths,” unpublished (2013).
[13] J. Miškuf and R. Sotk, “Total edge irregularity strength of complete graphs and complete bipartite graphs,” Electronic Notes in Discrete Mathematics, vol. 28, pp. 281-285 (2007).
[14] A. Rosa, “On certain valuations of the vertices of a graph,” in Theory of Graphs (Internat. Symposium, Rome), pp. 349-355, Jul (1966).
[15] I. Rosyida, E. Ningrum, M. Mulyono, and D. Indriati, “On the total edge irregularity strength of general uniform cactus chain graphs with pendant vertices,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 23, no. 6, pp. 1335-1358 (2020).
[16] D. Tanna, J. Ryan, and A. Semanicov-Fenovckova, “Edge irregular reflexive labeling of prisms and wheels,” Australasian Journal of Combinatorics, vol. 69, no. 3, pp. 394-401 (2017).

Views: 169Downloads: 73Citations: 0