Zk-magic labeling of star of graphs

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-01-0003

Keywords:

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

Abstract

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 Zk-magic graph if the group A is Zk, 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 Zk-magic graphs.

Author Biographies

P. Jeyanthi, Govindammal Aditanar College for Women.

Dept. of Mathematics.

K. Jeya Daisy, Holy Cross College.

PG and Research Dept. of Mathematics.

References

J. A. Gallian, “A Dynamic Survey of Graph Labeling”, 21th ed. The electronics journal of combinatorics, vol. # DS6, p. 502, 2007. [On line]. Available: https://bit.ly/2tE6Eow

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.

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: https://bit.ly/2ukchs4

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: https://bit.ly/2tFW6oL

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: https://bit.ly/36bXWel

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: https://bit.ly/2TLobpi

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: https://bit.ly/2Rd7bqv

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.

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: https://bit.ly/2Gamutw

J. Sedláček, “On magic graphs”, Mathematica slovaca, vol. 26, no. 4, pp. 329-335, 1976. [On line]. Available: https://bit.ly/38E4Yuf

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: https://bit.ly/3at77KO

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: https://bit.ly/2RERuY5

Published

2020-02-04

How to Cite

[1]
P. Jeyanthi and K. J. Daisy, “Zk-magic labeling of star of graphs”, Proyecciones (Antofagasta, On line), vol. 39, no. 1, pp. 31-50, Feb. 2020.

Issue

Section

Artículos