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Note on the group edge irregularity strength of graphs

Author

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  • Anholcer, Marcin
  • Cichacz, Sylwia

Abstract

We investigate the group edge irregularity strength (esg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group G of order s, there exists a function f:V(G)→G such that the sums of vertex labels at every edge are distinct. In this note we provide some the upper bounds on esg(G) as well as for edge irregularity strength es(G) and harmonious order har(G).

Suggested Citation

  • Anholcer, Marcin & Cichacz, Sylwia, 2019. "Note on the group edge irregularity strength of graphs," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 237-241.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:237-241
    DOI: 10.1016/j.amc.2019.01.007
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    References listed on IDEAS

    as
    1. Marcin Anholcer & Sylwia Cichacz & Martin Milanic̆, 2015. "Group irregularity strength of connected graphs," Journal of Combinatorial Optimization, Springer, vol. 30(1), pages 1-17, July.
    2. Xu, Changqing & Li, Jianguo & Ge, Shan, 2018. "Neighbor sum distinguishing total chromatic number of planar graphs," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 189-196.
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