Zk-Magic Labeling of Path Union of Graphs

  • P. Jeyanthi Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur 628215, Tamilnadu, India.
  • K. Jeya Daisy Department of Mathematics, Holy Cross College, Nagercoil, Tamilnadu, India.
  • Andrea Semaničová-feňovčíková Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic.
Keywords: A-magic labeling, Zk-magic labeling, Zk -magic graph, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle, n-pan 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) = ∑f(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 as k-magic graphs. In this paper we prove that the graphs such as path union of cycle, generalized Petersen graph, shell, wheel, closed helm, double wheel, flower, cylinder, total graph of a path, lotus inside a circle and n-pan graph are Zk-magic graphs.

References

[1] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Comb., 2018, # DS6.
[2] P. Jeyanthi and K. Jeya Daisy, Zk-magic labeling of subdivision graphs, Discrete Math. Algorithm. Appl., 8(3) (2016), 19 pages, DOI: 10.1142/ S1793830916500464.
[3] P. Jeyanthi and K. Jeya Daisy, Zk-magic labeling of open star of graphs, Bull. Inter. Math. Virtual Inst., 7 (2017), 243–255.
[4] P. Jeyanthi and K. Jeya Daisy, Certain classes of Zk-magic graphs, J. Graph Labeling, 4(1) (2018), 38–47.
[5] P. Jeyanthi and K. Jeya Daisy, Zk-magic labeling of some families of graphs, J. Algorithm Comput., 50(2) (2018), 1–12.
[6] P. Jeyanthi and K. Jeya Daisy, Zk-magic labeling of cycle of graphs, Int. J. Math. Combin., 1 (2019), 88–102.
[7] P. Jeyanthi and K. Jeya Daisy, Some results on Zk-magic labeling, Palestine J. Math., 8(2) (2019), 400–412.
[8] K. Kavitha and K. Thirusangu, Group magic labeling of cycles with a common vertex, Int. J. Comput. Algorithm, 2 (2013), 239–242.
[9] R.M. Low and S.M. Lee, On the products of group-magic graphs, Australas. J. Combin., 34 (2006), 41–48.
[10] J. Sedlacek, On magic graphs, Math. Slov., 26 (1976), 329–335.
[11] S.C. Shee and Y.S. Ho, The cordiality of the path-union of n copies of a graph, Discrete Math., 151(1-3) (1996), 221–229.
[12] W.C. Shiu, P.C.B. Lam and P.K. Sun, Construction of magic graphs and some A-magic graphs with A of even order, Congr. Numer., 167 (2004), 97–107.
[13] W.C. Shiu and R.M. Low, Zk-magic labeling of fans and wheels with magic-value zero, Aus- tralas. J. Combin., 45 (2009), 309–316.
Published
2019-10-15
How to Cite
Jeyanthi, P., Jeya Daisy, K., & Semaničová-feňovčíková, A. (2019). Zk-Magic Labeling of Path Union of Graphs. CUBO, A Mathematical Journal, 21(2), 15–40. https://doi.org/10.4067/S0719-06462019000200015