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Extending of Edge Even Graceful Labeling of Graphs to Strong r-Edge Even Graceful Labeling

Author

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  • Mohamed R. Zeen El Deen
  • Nora A. Omar
  • Antonio Di Crescenzo

Abstract

Edge even graceful labeling of a graph G with p vertices and q edges is a bijective f from the set of edge EG to the set of positive integers 2,4,…,2q such that all the vertex labels f∗VG, given by f∗u=∑uv∈EGfuvmod2k, where k=maxp,q, are pairwise distinct. There are many graphs that do not have edge even graceful labeling, so in this paper, we have extended the definition of edge even graceful labeling to r-edge even graceful labeling and strong r-edge even graceful labeling. We have obtained the necessary conditions for more path-related graphs and cycle-related graphs to be an r-edge even graceful graph. Furthermore, the minimum number r for which the graphs: tortoise graph, double star graph, ladder and diagonal ladder graphs, helm graph, crown graph, sunflower graph, and sunflower planar graph, have an r-edge even graceful labeling was found. Finally, we proved that the even cycle C2n has a strong 2-edge even graceful labeling when n is even.

Suggested Citation

  • Mohamed R. Zeen El Deen & Nora A. Omar & Antonio Di Crescenzo, 2021. "Extending of Edge Even Graceful Labeling of Graphs to Strong r-Edge Even Graceful Labeling," Journal of Mathematics, Hindawi, vol. 2021, pages 1-19, April.
    • Handle: RePEc:hin:jjmath:6643173
    DOI: 10.1155/2021/6643173
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    Cited by:

    1. Rakhi Das & Laxminarayan Sahoo & Sovan Samanta & Vladimir Simic & Tapan Senapati, 2022. "Identifying the Shortest Path of a Semidirected Graph and Its Application," Mathematics, MDPI, vol. 10(24), pages 1-13, December.

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