Grundy Dominating and Grundy Hop Dominating Sequences in Graphs: Relationships and Some Structural Properties

Authors

  • Javier Hassan MSU-Iligan Institute of Technology, 9200, Iligan City, Philippines
  • Sergio R. Canoy, Jr

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4690

Keywords:

Grundy dominating sequence, Grundy hop dominating sequence, Grundy domination number, Grundy hop domination number

Abstract

In this paper, we revisit the concepts of Grundy domination and Grundy hop domination in graphs and give some realization results involving these parameters. We show that the Grundy domination number and Grundy hop domination number of a graph G are generally incomparable (one is not always less than or equal the other). It is shown that their absolute difference can be made arbitrarily large. Moreover, the Grundy domination numbers of some graphs are determined.

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Published

2023-04-30

Issue

Vol. 16 No. 2: (April 2023)

Section

Nonlinear Analysis

License

Copyright (c) 2023 European Journal of Pure and Applied Mathematics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Grundy Dominating and Grundy Hop Dominating Sequences in Graphs: Relationships and Some Structural Properties. (2023). European Journal of Pure and Applied Mathematics, 16(2), 1154-1166. https://doi.org/10.29020/nybg.ejpam.v16i2.4690

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