Γ-supermagic labeling of products of two cycles with cyclic groups

Dalibor Froncek

Abstract


A Γ-supermagic labeling of a graph G=(V,E) is a bijection from E to a group Γ of order |E| such that the sum of labels of all edges incident with any vertex x∈ V is equal to the same element μ ∈ Γ.

A Z2mn-supermagic labeling of the Cartesian product of two cycles, Cm ℺ Cn for every m,n ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a Zk-supermagic labeling of the direct and strong product by cyclic group Zk for any m,n ≥ 3.

Keywords


Magic-type labeling, supermagic labeling, vertex-magic edge labeling, group supermagic labeling

Full Text:

PDF

DOI: http://dx.doi.org/10.19184/ijc.2023.7.1.3

References

D. Froncek, Supermagic labelings of Cn ℺ Cm, unpublished manuscript.

D. Froncek, J. McKeown, J. McKeown, M. McKeown, Z2nm-supermagic labeling of Cn ℺ Cm, Indones. J. Combin., 2(2) (2018), 57--71.

D. Froncek, M. McKeown, Note on diagonal construction of Z2nm-supermagic labeling of Cn ℺ Cm, AKCE Int. J. Graphs Comb., 17(3) (2020), 952--954.

D. Froncek, P. Paananen, L. Sorensen, Group-supermagic labeling of Cartesian product of two odd cycles, Bull. Inst. Combin. Appl., accepted.

D. Froncek, P. Paananen, L. Sorensen, Group-supermagic labeling of Cartesian product of two even cycles, submitted.

J. Ivanco, On supermagic regular graphs, Math. Bohem., 125 (2000), 99--114.

P. Paananen, Γ-supermagic Labeling of Cm ℺ Cn, MS Thesis, University of Minnesota Duluth, Duluth, MN, U.S.A., 2021.

J. Sedlacek, Problem 27, in: M. Fiedler (Ed.), Theory of Graphs and Its Applications, Praha, 1964, pp.163–164.

L. Sorensen, Γ-supermagic Labeling of Cm ℺ Cn, MS Thesis, University of Minnesota Duluth, Duluth, MN, U.S.A., 2020.

R. Stanley, Linear homogeneous diophantine equations and magic labelings of graphs, Duke Math. J., 40 (1973), 607--632.

R. Stanley, Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings, Duke Math. J., 43 (1976), 511--531.

B. M. Stewart, Magic graphs, Canad. J. Math., 18 (1996), 1031--1059.

P. M. Weichsel, The Kronecker product of graphs, Proc. Amer. Math. Soc., 13 (1962), 47--52.


Refbacks

  • There are currently no refbacks.


ISSN: 2541-2205

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

View IJC Stats