On D-distance (anti)magic labelings of shadow graph of some graphs

Anak Agung Gede Ngurah, Nur Inayah, Mohamad Irvan Septiar Musti

Abstract


Let G be a graph with vertex set V(G) and diameter diam(G). Let D ⊆ {0, 1, 2, 3, …, diam(G)} and φ : V(G)→{1, 2, 3, …, |V(G)|} be a bijection. The graph G is called D-distance magic, if  s ∈ ND(t)φ(s) is a constant for any vertex t ∈ V(G). The graph G is called (α, β)-D-distance antimagic, if { s ∈ ND(t)φ(s):t ∈ V(G)} is a set {α, α + β, α + 2β, …, α + (|V(G)| − 1)β}. In this paper, we study D-distance (anti)magic labelings of shadow graphs for D = {1}, {0, 1}, {2}, and {0, 2}.


Keywords


D-distance (anti)magic labeling, D-distance (anti)magic graph, shadow graph

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DOI: http://dx.doi.org/10.5614/ejgta.2024.12.1.3

References

S. Arumugam and N. Kamatchi, On (a, d)-distance antimagic graphs, Australas J. Combin. 54 (2012), 279 – 287.

S. Beena, On and ′ labelled graphs, Discrete Math. 309 (2009), 1783 – 1787.

D. Froncek, Handicap distance antimagic graphs and incomplete tournaments, AKCE Int. J. Graphs and Combin. 10 (2013), 119 – 127.

B. Freyberg and M. Keranen, Orientable Zn-distance magic labeling of the Cartesian product of many cycles, Electron. J. Graph Theory Appl. 5(2) (2017), 304 – 311.

D. Froncek and A. Shepanik, Regular handicap graphs of order n ≡ 0 (mod 8), Electron. J. Graph Theory Appl. 6(2) (2018), 208 – 218.

J. Gallian, A dynamic survey of graph labeling, The Electronic J. of Combinat. 25 (2022), #DS6.

N. Kamatchi and S. Arumugam, Distance antimagic graphs, J. Combin. Math. Combin. Comput. 84 (2013), 61 -– 67.

N. Kamatchi, G.R. Vijayakumar, A. Ramalakshmi, S. Nilavarasi, and S. Arumugam, 2016, Distance antimagic labelings of graphs, ICTCSDM 2016: First International Conference on Theoretical Computer Science and Discrete Mathematics, Krishnankoil, India, 19–21 December.

C. Krisna and S. Perikamana, 2021, Distance magic labeling on shadow graphs, ICMTA 2021: 2nd International Conference on Mathematical Techniques and Applications, Kattankulathur, India, 24–26 March.

M. Miller, C. Rodger, and R. Simanjuntak, Distance magic labelings of graphs, Australas. J. Combin. 28 (2003), 305 -– 315.

A. O’Neal and P. Slater, An introduction to distance D-magic graphs, J. Indones. Math. Soc. Special Edition (2011), 89 – 107.

A. O’Neal and P. Slater, Uniqueness of vertex magic constants, SIAM J. Discrete Math. 27 (2013), 708 – 716.

A.A.G. Ngurah and N. Inayah, 2022, On {0, 1}-distance labelings of 2-regular graphs, ICoMCoS 2022: International Conference on Mathematics, Computational Sciences and Statistics, Surabaya, Indonesia, 3 October.

A.A.G. Ngurah and R. Simanjuntak, On Distance labelings of 2-regular graphs, Electron. J. Graph Theory Appl. 9(1) (2021), 25 – 37.

R. Simanjuntak and K. Wijaya, On distance antimagic graphs, arXiv:1312.7405.

K.A. Sugeng, D. Froncek, M. Miller, J. Ryan, and J. Walker, On distance magic labeling of graphs, J. Combin. Math. Combin. Comput. 71 (2009), 39 –- 48.

V. Vilfred, -labelled Graph and Circulant Graphs, Ph.D. Thesis, University of Kerala, Trivandrum, India, 1994.


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