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Modular irregularity strength of dense graphs

I Nengah Suparta, Made Candiasa, Kadek Wahyu Prasancika, Martin Baca

Abstract


We solve the open problem posed in Modular irregularity strength of graphs, Electron. J. Graph Theory and Appl. 8 (2020), 435–433, asking about the modular irregularity strength of the complete graph Kn for all n ≥ 3. Furthermore, we establish also the exact values of the modular irregularity strength of complete bipartite graphs Kn, n + t for any positive integer n and t = 0, 1, 2.

Keywords


complete graph, complete bipartite graph, irregular labeling, modular irregularity strength

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DOI: http://dx.doi.org/10.5614/ejgta.2024.12.1.9

References

M. Aigner and E. Triesch, Irregular assignments of trees and forests, SIAM J. Discrete Math. 3 (1990), 439–449.

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

M. Bača, Z. Kimáková, M. Lascsáková, and A. Semaničová-Feňovčíková, The irregularity and modular irregularity strength of fan graphs, Symmetry 13(4) (2021), 605, 13 pages.

M. Bača, K. Muthugurupackiam, K.M. Kathiresan, and S. Ramya, Modular irregularity strength of graphs, Electron. J. Graph Theory Appl. 8 (2) (2020), 435–433.

T. Bohman and D. Kravitz, On the irregularity strength of trees, J. Graph Theory 45 (2004), 241–254.

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

A. Frieze, R.J. Gould, M. Karonski, and F. Pfender, On graph irregularity strength, J. Graph Theory 41 (2002), 120–137.

M. Kalkowski, M. Karonski, and F. Pfender, A new upper bound for the irregularity strength of graphs, SIAM J. Discrete Math. 25(3) (2011), 1319–1321.

P. Majerski and J. Przybylo, On the irregularity strength of dense graphs, SIAM J. Discrete Math. 28 (1) (2014), 197–205.

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

J. Przybylo, Irregularity strength of regular graphs, Electron. J. Combin. 15 (2008), R82.

K.A. Sugeng, P. John, M.L. Lawrence, L.F. Anwar, M. Bača, and A. Semaničová-Feňovčíková, Modular irregularity strength on some flower graphs, Electron. J. Graph Theory Appl., 11 (1) (2023), 27–38.


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ISSN: 2338-2287

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