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Antimagicness of Lexicographic Product Graph G[Pn]

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Abstract

Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic. Since then, many classes of graphs have been proved to be antimagic. But few is known about the antimagicness of lexicographic product graphs. In this paper, via the construction of a directed Eulerian circuit, the Siamese method, and some modification on graph labeling, the antimagicness of lexicographic product graph G[Pn] is obtained.

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Acknowledgments

The authors thank the referees for their careful reading of the paper, and for their valuable comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

    Ying-yu Lu & Guang-hua Dong

  2. Lushan College of Guangxi University of Science and Technology, Liuzhou, 545000, China

    Ying-yu Lu

  3. Department of Information Science and Technology, Tianjin University of Finance and Economics, Tianjin, 300222, China

    Ning Wang

Authors
  1. Ying-yu Lu
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  2. Guang-hua Dong
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  3. Ning Wang
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Corresponding author

Correspondence to Guang-hua Dong.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos. 11401430).

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Lu, Yy., Dong, Gh. & Wang, N. Antimagicness of Lexicographic Product Graph G[Pn]. Acta Math. Appl. Sin. Engl. Ser. 36, 603–619 (2020). https://doi.org/10.1007/s10255-020-0953-0

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  • DOI: https://doi.org/10.1007/s10255-020-0953-0

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