SciELO - Scientific Electronic Library Online

vol.39 número1Nondifferentiable higher-order duality theorems for new type of dual model under generalized functionsPartition of the spectra for the lower triangular double band matrix as generalized difference operator Δ v over the sequence spaces c and 𝓵 p (1 < p < ∞) índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta feb. 2020 


Zk-Magic Labeling of Star of Graphs

1 Govindammal Aditanar College for Women, Dept. of Mathematics Tiruchendur, TN, India. E-mail:

2 Holy Cross College, PG and Research Dept. of Mathematics, Nagercoil, TN, India. E-mail:


For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f + defined as f + (v) = Pf(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Z k -magic graph if the group A is Z k , the group of integers modulo k and these graphs are referred to as k-magic graphs. In this paper we prove that the graphs such as star of cycle, flower, double wheel, shell, cylinder, gear, generalised Jahangir, lotus inside a circle, wheel, closed helm graph are Z k -magic graphs.

Keywords: A-magic labeling; Flower; Double wheel; Shell; Cylinder; Gear; Generalised Jahangir; Lotus inside a circle; Wheel; Closed helm graph

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

[1] J. A. Gallian, “A Dynamic Survey of Graph Labeling”, 21th ed. The electronics journal of combinatorics, vol. # DS6, p. 502, 2007. [On line]. Available: ]

[2] P. Jeyanthi and K. J. Daisy, “Zk-Magic labeling of subdivision graphs”, Discrete mathematics, algorithms and applications, vol. 8, no. 3, Art. ID 1650046, Jun. 2016, doi: 10.1142/ S1793830916500464. [ Links ]

[3] P. Jeyanthi and K. Jeya Daisy, “Zk-magic labeling of open star of graphs”, Bulletin of the international mathematical virtual institute, vol. 7, no. 2, pp. 243-255, 2017. [On line]. Available: ]

[4] P. Jeyanthi and K. Jeya Daisy, “Certain classes of Zk-magic graphs”, Journal of graph labeling, vol. 4, no. 1, pp. 38-47, 2018. [On line]. Available: ]

[5] P. Jeyanthi and K. Jeya Daisy, “Zk-magic labeling of some families of graphs”, Journal of algorithms and computation, vol. 50, no. 2, pp. 1-12, Dec. 2018. [On line]. Available: ]

[6] P. Jeyanthi and K. Jeya Daisy, “Zk-magic labeling of cycle of graphs”, International journal of mathematical combinatorics, vol. 1, pp. 88- 102, Mar. 2019. [On line]. Available: Links ]

[7] P. Jeyanthi and K. Jeya Daisy, “Some results on Zk-magic labeling”, Palestine journal of mathematics, vol. 8, no. 2, pp. 400-412, 2019. [On line]. Available: ]

[8] P. Jeyanthi, K. J. Daisy, and A. Semanicová-Fenovníková, “Zk-magic labeling of path union of graphs”, Cubo (Temuco), vol. 21, no. 2, pp. 15-35, Aug. 2019, doi: 10.4067/s0719-06462019000200015. [ Links ]

[9] R. M. Low and S. M. Lee, “On the products of group-magic graphs”, Australasian journal of combinatorics, vol. 34, pp. 41-48, Feb. 2006. [On line]. Available: ]

[10] J. Sedláček, “On magic graphs”, Mathematica slovaca, vol. 26, no. 4, pp. 329-335, 1976. [On line]. Available: ]

[11] W. C. Shiu, P.C.B. Lam, and P. K. Sun, “Construction of group-magic graphs and some A-magic graphs with A of even order”, Congressus numerantium, vol. 167, pp. 97-107, 2004. [On line]. Available: ]

[12] W. C. Shiu and R. M. Low, “Zk-magic labeling of fans and wheels with magic-value zero”, Australasian journal of combinatorics , vol. 45, pp. 309-316, Oct. 2009. [On line]. Available: Links ]

Received: November 2018; Accepted: April 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License