On Efficient Zero Ring Labeling and Restricted Zero Ring Graphs

Authors

  • Francis Joseph Hernandez Campena De La Salle University, Manila https://orcid.org/0000-0002-6037-6769
  • Dhenmar Chua Adamson University, Manila
  • Floresto Franco, Jr. Mariano Marcos State University, Batac Ilocos Norte
  • Jon-jon Casica De La Salle University, Manila

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i1.3890

Keywords:

efficient zero ring labeling, zero ring labeling, zero ring

Abstract

In [3], Acharya et al. introduced the notion of a zero ring labeling of a connected
graph G, where vertices are labeled by the elements of a zero ring such that the sum of the labels of adjacent vertices is not the additive identity of the ring. Archarya and Pranjali [1] also constructed a graph based on a finite zero ring called the zero ring graph. In [5], Chua et al. defined a class of zero ring labeling called efficient zero ring labeling and it was shown that a labeling scheme exists for some families of trees. In this paper, we provide an efficient zero ring labeling for some classes of graphs. We also introduce the notion of the restricted zero ring graphs and use them to show that a zero ring labeling exists for some classes of cactus graphs.

Author Biographies

  • Francis Joseph Hernandez Campena, De La Salle University, Manila
         

    Mathematics and Statistics Department

    Assistant Professor

  • Dhenmar Chua, Adamson University, Manila
      Mathematics and Physics Department 
  • Floresto Franco, Jr., Mariano Marcos State University, Batac Ilocos Norte
     Mathematics Department 
  • Jon-jon Casica, De La Salle University, Manila
     Mathematics and Statistics Department

Downloads

Published

2021-01-31

Issue

Vol. 14 No. 1: (January 2021)

Section

Nonlinear Analysis

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On Efficient Zero Ring Labeling and Restricted Zero Ring Graphs. (2021). European Journal of Pure and Applied Mathematics, 14(1), 268-277. https://doi.org/10.29020/nybg.ejpam.v14i1.3890