\(Z_k\)-magic labeling of path union of graphs
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P. Jeyanthi
jeyajeyanthi@rediffmail.com
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K. Jeya Daisy
jeyadaisy@yahoo.com
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Andrea SemaniÄová-feňovÄíková
andrea.fenovcikova@tuke.sk
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DOI:
https://doi.org/10.4067/S0719-06462019000200015Abstract
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.
Keywords
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[6] P. Jeyanthi and K. Jeya Daisy, Zk-magic labeling of cycle of graphs, Int. J. Math. Combin., 1 (2019), 88–102.
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[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.
[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.
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Published
2019-08-10
How to Cite
[1]
P. Jeyanthi, K. . Jeya Daisy, and A. . SemaniÄová-feňovÄíková, “\(Z_k\)-magic labeling of path union of graphs”, CUBO, vol. 21, no. 2, pp. 15–40, Aug. 2019.
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