Distance Antimagic Labeling for Copies of Graph

Authors

  • Peter John Universitas Indonesia
  • Bonardo Lubis Universitas Indonesia
  • Kiki Ariyanti Sugeng Universitas Indonesia

DOI:

https://doi.org/10.25077/jmua.15.3.319-324.2026

Keywords:

distance antimagic labeling, distance antimagic graph, copies of graph

Abstract

Let G be a graph with vertex set V(G) and edge set E(G). Let f be a bijective function from the vertex set V(G) to the set {1,2,3,... ,|V(G)|} and weight of vertex v in V(G) is the sum of labels of all neighbors of vertex v. If there is no pair of vertices of V(G) have equal weight, then f is called a distance antimagic labeling and G is called a distance antimagic graph. Copies of graph G, denoted as nG is disjoint union of n graphs which each is isomorphic to G. In this paper, we present several results on distance antimagic labeling of copies of graph.

References

[1] Kamachi, N., Arumugam, S., 2013, Distance Antimagic Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 84: 61–67

[2] Handa, A.K., Godinho, A., Singh, T., 2016, Some Distance Antimagic Labeled Graphs, Algorithms and Discrete Applied Mathematics, Vol. 9602: 190–200

[3] Handa, A.K., Godinho, A., Singh, T., Arumugam, S., 2017, Distance antimagic labeling of join and corona of two graphs, AKCE International Journal of Graphs and Combinatorics, Vol. 14(2): 172–177

[4] Simanjuntak, R., Nadeak, T., Yasin, F., Wijaya, K., Hinding, M., Sugeng, K.A., 2021, Another Antimagic Conjecture, Symmetry, Vol. 13: 2071

[5] Simanjuntak, R., Tritama, A., 2022, Distance Antimagic Product Graphs, Symmetry, Vol. 14: 1411

[6] Burr, A., Erdos, P., Spencer, J.H., 1975, Ramsey theorems for multiple copies of graphs, Transactions Of The American Mathematical Society, Vol. 209: 87–99

[7] Gallian, J.A., 2024, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, Vol. 17

[8] West, D.B., 2001, Introduction to Graph Theory, 2nd, Prentice Hall

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Published

31-07-2026

Issue

Vol. 15 No. 3 (2026)

Section

Articles

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