Modular irregularity strength on some flower graphs
Abstract
Let G = (V(G),E(G)) be a graph with the nonempty vertex set V(G) and the edge set E(G). Let Zn be the group of integers modulo n and let k be a positive integer. A modular irregular labeling of a graph G of order n is an edge k-labeling φ : E(G)→{1, 2, …, k}, such that the induced weight function σ : V(G)→Zn defined by σ(v) = Σ (u∈N(v)) φ(uv) (mod n) for every vertex v ∈ V(G) is bijective. The minimum number k such that a graph G has a modular irregular k-labeling is called the modular irregularity strength of a graph G, denoted by ms(G). In this paper, we determine the exact values of the modular irregularity strength of some families of flower graphs, namely rose graphs, daisy graphs and sunflower graphs.
Keywords
Full Text:
PDFDOI: http://dx.doi.org/10.5614/ejgta.2023.11.1.3
References
M. Aigner and E. Triesch, Irregular assignments of trees and forests, SIAM J. Discrete Math. 3 (1990), 439–449.
D. Amar and O. Togni, Irregularity strength of trees, Discrete Math. 190 (1998), 15–38.
M. Bača, M. Imran, and A. Semaničová-Feňovčíková, Irregularity and modular irregularity strength of wheels, Mathematics 9 (2021), 2710, 14 pages.
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 (2020), 435–443.
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.
R.J. Faudree, M.S. Jacobson, J. Lehel, and R.H. Schelp, Irregular networks, regular graphs and integer matrices with distinct row and column sums, Discret. Math. 76 (1989), 223–240.
A. Frieze, R.J. Gould, M. Karonski, and F. Pfender, On graph irregularity strength, J. Graph Theory 41 (2002), 120–137.
D. Indriati, W. Widodo, I.E. Wijayanti, K.A. Sugeng, and I. Rosyida, Totally irregular total labeling of some caterpillar graphs, Electron. J. Graph Theory Appl. 8 (2020), 247–254.
M. Kalkowski, M. Karonski,and F. Pfender, A new upper bound for the irregularity strength of graphs, SIAM J. Discret. Math. 25 (3) (2011), 1319–1321.
P. Majerski and J. Przybyło, On the irregularity strength of dense graphs, SIAM J. Discret. Math. 28 (2014), 197–205.
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), 415–421.
K.A. Sugeng, Z.Z. Barack, N. Hinding, and R. Simanjuntak, Modular irregular labeling on double-star and friendship graphs, J. Math. 2021 (2021), art. no. 4746609, 6 pages.
Refbacks
- There are currently no refbacks.
ISSN: 2338-2287
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.