Outer-connected Hop Dominating Sets in Graphs

Authors

  • Chrisley Jade Saromines Mindanao State University - Iligan Institute of Technology
  • Sergio Canoy, Jr. Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i4.4590

Keywords:

hop domination, outer-connected, join, corona, lexicographic product

Abstract

Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. A hop dominating set S ⊆ V (G) is called an outer-connected hop dominating set if S = V (G) or the subgraph ⟨V (G) \ S⟩ induced by V (G) \ S is connected. The minimum size of an outer-connected hop dominating set is the outer-connected hop domination number γfch(G). A dominating set
of size γfch(G) of G is called a γfch-set. In this paper, we investigate the concept and study it for graphs resulting from some binary operations. Specifically, we characterize the outer-connected hop dominating sets in the join, corona and lexicographic products of graphs, and determine bounds of the outer-connected hop domination number of each of these graphs.

Author Biography

  • Sergio Canoy, Jr., Mindanao State University-Iligan Institute of Technology

    Professor Sergio Canoy is affiliated in Department of Mathematics and Statistics, College of Science and Mathematics, Center for Graph Theory, Algebra and Analysis-PRISM, MSU-Iligan Institute of Technology, 9200, Iligan City, Philippines

Downloads

Published

2022-10-31

Issue

Vol. 15 No. 4: (October 2022)

Section

Nonlinear Analysis

License

Copyright (c) 2022 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 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

Outer-connected Hop Dominating Sets in Graphs. (2022). European Journal of Pure and Applied Mathematics, 15(4), 1966-1981. https://doi.org/10.29020/nybg.ejpam.v15i4.4590