On reflexive edge strength of generalized prism graphs

Muhammad Irfan, Martin Baca, Andrea Semanicova-Fenovcikova


Let G be a connected, simple and undirected graph. The assignments {0, 2, …, 2kv} to the vertices and {1, 2, …, ke} to the edges of graph G are called total k-labelings, where k = max{ke, 2kv}. The total k-labeling is called an reflexive edge irregular k-labeling of the graph G, if for every two different edges xy and xy′ of G, one has

wt(xy)=fv(x)+fe(xy)+fv(y)≠wt(xy′) = fv(x′) + fe(xy′) + fv(y′).

The minimum k for which the graph G has an reflexive edge irregular k-labeling is called the reflexive edge strength of G. In this paper we investigate the exact value of reflexive edge strength for generalized prism graphs.


reflexive edge irregular labeling, reflexive edge strength, generalized prism graph

Full Text:


DOI: http://dx.doi.org/10.5614/ejgta.2022.10.2.6


A. Ahmad, M. Bača, and M. Numan, On irregularity strength of disjoint union of friendship graphs, Electron. J. Graph Theory Appl. 1(2) (2013), 100–108.

D. Amar and O. Togni, Irregularity strength of trees, Discrete Math. 190 (1998), 15–38.

M. Anholcer and C. Palmer, Irregular labelings of circulant graphs, Discrete Math. 312(23) (2012), 3461–3466.

F. Ashraf, M. Bača, A. Semaničová-Feňovčíková, and S.W. Saputro, On cycle-irregularity strength of ladders and fan graphs, Electron. J. Graph Theory Appl. 8(1) (2020), 181–194.

M. Bača, M. Irfan, and J. Ryan, A. Semaničová-Feňovčíková and D. Tanna, Note on edge irregular reflexive labelings of graphs, AKCE J. Graphs. Combin. 16(2) (2019), 145–157.

M. Bača, M. Irfan, and J. Ryan, A. Semaničová-Feňovčíková and D. Tanna, On edge irregular reflexive labellings for the generalized friendship graphs, Mathematics 5(4) (2017), 67.

M. Bača, S. Jendro, M. Miller, and J. Ryan, Total irregular labelings, Discrete Math. 307 (2007), 1378–1388.

M. Bača, and M.K. Siddiqui, Total edge irregularity strength of generalized prism, Appl. Math. Comput. 235 (2014), 168–173.

S. Brandt, J. Miškuf, and D. Rautenbach, On a conjecture about edge irregular total labellings, J. Graph Theory 57 (2008), 333–343.

G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz, and F. Saba, Irregular networks, Cong. numer. 64 (1988), 187–192.

J.H. Dimitz, D.K. Garnick, and A. Gyárfás, On the irregularity strength of the m × n grid, J. Graph Theory 16 (1992), 355–374.

A. Gyárfás, The irregularity strength of Km, m is 4 for odd m, Discrete Math. 71 (1998), 273–274.

D. Indriati, Widodo, I.E. Wijayanti, K.A. Sugeng, and I. Rosyida, Totally irregular total labeling of some caterpillar graphs, Electron. J. Graph Theory Appl. 8 (2) (2020), 247–254.

J. Ivančo and S. Jendro, Total edge irregularity strength of trees, Discuss. Math. Graph Theory 26 (2006), 449–456.

S. Jendro, J. Miškuf, and R. Soták, Total edge irregularity strength of complete and complete bipartite graphs, Electron. Notes Discrete Math. 28 (2007), 281–285.

J. Lehel, Facts and quests on degree irregular assignment, Graph Theory, Combin. Appl., Wiley, New York, 1991, p.p. 765–782.

T. Nierhoff, A tight bound on the irregularity strength of graphs, SIAM J. Discrete Math. 13 (2000), 313–323.

J. Ryan, B. Munasinghe, A. Semaničová-Feňovčíková, and D. Tanna, Reflexive irregular labelings, submitted.

M.K. Siddiqui, On the total edge irregularity strength of a categorical product of a cycle and a path, AKCE J. Graphs. Combin. 9(1) (2012), 43–52.

D. Tanna, J. Ryan, and A. Semaničová-Feňovčíková, Edge irregular reflexive labeling of prisms and wheels, Australas. J. Comb. 69(3) (2017), 394–401.


  • There are currently no refbacks.

ISSN: 2338-2287

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View EJGTA Stats