Abstract
A labeling f of a graph G is a bijection from its edge set E(G) to the set \(\{1, 2, \ldots , |E(G)|\}\), which is antimagic if the vertex-sums are pairwise distinct, where the vertex-sum at one vertex is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling f. In this paper, we show that the graph \(K_{m,n}[P_{k}]\), which is the lexicographic product of the complete bipartite graph \(K_{m,n}\) and path \(P_{k}\), is antimagic.
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This work was Supported by the National Natural Science Foundation of China (Grant Nos: 11301381 and 11401430).
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Lu, Y., Dong, G., Ma, W. et al. Antimagic Labeling of the Lexicographic Product Graph \(K_{m,n}[P_k]\) . Math.Comput.Sci. 12, 77–90 (2018). https://doi.org/10.1007/s11786-017-0327-z
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DOI: https://doi.org/10.1007/s11786-017-0327-z